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pdfUnited States
Department
of Agriculture
Forest Service
Rocky Mountain
Research Station
General Technical
Report RMRS-GTR-56
October 2000
Wilderness Recreation Use
Estimation: A Handbook of
Methods and Systems
Alan E. Watson
David N. Cole
David L. Turner
Penny S. Reynolds
Abstract _________________________________________
Watson, Alan E.; Cole, David N.; Turner, David L.; Reynolds, Penny S. 2000. Wilderness recreation
use estimation: a handbook of methods and systems. Gen. Tech. Rep. RMRS-GTR-56. Ogden,
UT: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. 198 p.
Documented evidence shows that managers of units within the U.S. National Wilderness
Preservation System are making decisions without reliable information on the amount, types, and
distribution of recreation use occurring at these areas. There are clear legislative mandates and
agency policies that direct managers to monitor trends in use and conditions in wilderness. This
report is specifically designed as a convenient resource for wilderness managers and others who
have the responsibility of monitoring and describing visitor use in wilderness. It is a comprehensive
manual on estimation techniques and procedures that are essential to appropriately and accurately
measure visitor use-related characteristics and conditions. Guidelines enable the manager to
evaluate options and decide on a use estimation system that meets the needs of a specific area and
set of circumstances. This handbook provides, in a single source, all relevant information on setting
objectives, making decisions about what to monitor, developing a sampling plan, collecting the
needed information, and computing basic statistics to provide input into management decisions. The
user should have mathematical abilities at least through algebra; knowledge of statistics and
calculus would be helpful.
Keywords: National Wilderness Preservation System, visitation, visitor use, visitor use estimation
The Authors ____________________
Alan E. Watson is Research Social Scientist with the
Aldo Leopold Wilderness Research Institute on the University of Montana campus, Missoula. Dr. Watson’s
academic training was with the School of Forestry and
Wildlife Resources, Virginia Polytechnic Institute and
State University, including a Ph.D. degree in 1983. His
research interests are primarily in the area of wilderness
experience quality, including influences of conflict, solitude, and visitor impacts.
David N. Cole is Research Biologist with the Aldo
Leopold Wilderness Research Institute, Missoula, MT.
Dr. Cole received his B.A. degree in geography from the
University of California, Berkeley, in 1972. He received
his Ph.D. degree, also in geography, from the University
of Oregon in 1977. He has written many papers on
wilderness management, particularly the ecological effects of recreational use.
David L. Turner is Mathematical Statistician with the
Rocky Mountain Research Station in Logan, UT. Dr.
Turner received his education at Colorado State University, Fort Collins, including a Ph.D. degree in statistics in
1975.
Penny S. Reynolds is Assistant Professor of Comparative Physiology at the University of Richmond, VA.
Dr. Reynolds has a B.Sc. degree in wildlife biology and an
M. Sc. degree in zoology, both from the University of
Guelph, and an M.S. degree in biometry, and a Ph.D.
degree in zoology with a statistics minor (1992) from the
University of Wisconsin-Madison.
Acknowledgments ______________
The authors gratefully acknowledge cooperation and
support of the Southern Region of the USDA Forest
Service for providing the opportunity to work closely with
managers of that Region’s Cohutta Wilderness and Mount
Rogers National Recreation Area, and to explore in depth
the challenges of wilderness use estimation. Specific
acknowledgements go to Larry Phillips of the Southern
Region Office; Bill Black, Larry Thomas, and Mike Davis
of the Cohutta District of the Chattahoochee National
Forest; Tim Eling, Mike Evans and Steve Sherwood of
the Mount Rogers National Recreation Area, Jefferson
National Forest; and Harry Fisher of the Forest
Supervisor’s Office, Jefferson National Forest.
Rocky Mountain Research Station
324 25th Street
Ogden, UT 84401
Wilderness Recreation Use
Estimation: A Handbook of
Methods and Systems
Alan E. Watson
David N. Cole
David L. Turner
Penny S. Reynolds
Contents __________________________________________
Page
Introduction ........................................................................................................................ 1
The Problem: Inadequate Wilderness Use Data ............................................................ 2
What is a Wilderness Use Estimation System? .............................................................. 2
Handbook Organization ..................................................................................................... 3
Part I: Elements of a Use Estimation System ................................................................ 5
Chapter 1: Visitor Use Characteristics ............................................................................... 7
Objectives .......................................................................................................................... 7
Identification of Visitor Use Characteristics ........................................................................ 9
Visit Counts ................................................................................................................... 10
Individual Visits .......................................................................................................... 10
Group Visits ............................................................................................................... 10
Visit Attributes ............................................................................................................... 11
Method of Travel ........................................................................................................ 11
Group Size ................................................................................................................. 12
Use of Commercial Services ..................................................................................... 12
Activity Participation .................................................................................................. 13
Length of Stay ........................................................................................................... 13
Temporal Use Distribution ......................................................................................... 14
Spatial Use Distribution ............................................................................................. 14
Conditions and Visitor Perceptions ............................................................................ 14
Miscellaneous Visit Characteristics ........................................................................... 15
Visitor Attributes ............................................................................................................ 15
Sociodemographics ................................................................................................... 15
Past Experience ........................................................................................................ 16
Visitor Knowledge ...................................................................................................... 17
Visitor Attitudes and Preferences .............................................................................. 17
Summary-Use Statistics ............................................................................................... 18
Visitors ....................................................................................................................... 18
Visitor-Day ................................................................................................................. 18
Visitor-Hours .............................................................................................................. 18
Overnight Stays ......................................................................................................... 19
Recreation Visitor-Days ............................................................................................. 19
Chapter 2: Visitor Use Estimation Techniques ................................................................. 20
External Visual Observations ........................................................................................... 20
Internal Visual Observations: Stationary .......................................................................... 23
Internal Visual Observation: Roaming .............................................................................. 24
Mechanical Traffic Counters ............................................................................................ 24
Registration ...................................................................................................................... 29
Permits ............................................................................................................................ 32
Visitor Surveys ................................................................................................................. 36
Indirect Estimation ............................................................................................................ 39
Aerial Surveys .................................................................................................................. 41
Chapter 3: Sampling Methods .......................................................................................... 43
Convenience or Judgment Sampling ............................................................................... 43
Statistical Sampling Designs ............................................................................................ 44
Why Use Statistical Sampling? ..................................................................................... 44
What is a Good Sampling Design? ............................................................................... 44
Sample Size Determination .............................................................................................. 45
Defining the Sampling Unit ........................................................................................... 45
Sample Size .................................................................................................................. 46
Sampling Designs ............................................................................................................ 57
Page
Simple Random Sampling ............................................................................................ 47
How to Obtain a Random Sample ............................................................................. 47
Procedure for Random Sampling .............................................................................. 47
Advantages of Random Sampling ............................................................................. 49
Disadvantages of Random Sampling ........................................................................ 49
Systematic Sampling .................................................................................................... 49
Procedure for Systematic Sampling .......................................................................... 49
Advantages of Systematic Sampling ......................................................................... 49
Disadvantages of Systematic Sampling .................................................................... 49
Computations for Systematic Samples ...................................................................... 50
Multiple Systematic Sampling .................................................................................... 50
Computations for Multiple Systematic Samples ........................................................ 50
Stratified Sampling ........................................................................................................ 52
Procedure for Stratified Sampling .............................................................................. 53
Choosing Stratum Sample Size ................................................................................. 53
Advantages of Stratified Sampling ............................................................................ 53
Disadvantages of Stratified Sampling ........................................................................ 53
Computations for Stratified Samples ......................................................................... 54
Cluster Sampling .......................................................................................................... 54
Procedure for Cluster Sampling ................................................................................ 55
Advantages of Cluster Sampling ............................................................................... 55
Disadvantages of Cluster Sampling .......................................................................... 55
Effects of Sample Design on Use Estimates: A Case Study ........................................ 55
Field Sampling Strategies ............................................................................................. 57
Scheduling “Observer” Rotation Across Trailheads .................................................. 57
Scheduling Observer Effort ....................................................................................... 59
Calibration ................................................................................................................. 59
Compliance Estimates ............................................................................................... 60
Visitor Selection ......................................................................................................... 61
Part II: Selecting and Building a Use Estimation System .......................................... 63
Introduction ...................................................................................................................... 65
System A: Mechanical Counters With Visual Calibration ................................................. 68
System Description .......................................................................................................... 68
Operational Procedures ................................................................................................... 68
Step 1: Decide on Use Characteristics ......................................................................... 68
Step 2: Decide on Counter Type .................................................................................. 68
Step 3: Decide on the Number of Counters Needed .................................................... 70
Step 4: Choose the Calibration Method ........................................................................ 70
Step 5: Develop a Sampling Plan ................................................................................. 71
Step 6: Purchase Equipment ........................................................................................ 71
Step 7: Install Equipment .............................................................................................. 71
Step 8: Collect Calibration Data .................................................................................... 72
Step 9: Collect Counter Data ........................................................................................ 73
Step 10: Estimate Use .................................................................................................. 73
System B: Mechanical Counters With Observer Calibration and
Sample Observations ................................................................................................ 79
System Description .......................................................................................................... 79
Operational Procedures ................................................................................................... 79
Step 1: Decide on Use Characteristics ......................................................................... 79
Step 2: Decide on Counter Type .................................................................................. 80
Step 3: Decide on the Number of Counters Needed .................................................... 81
Step 4: Choose the Calibration Method ........................................................................ 81
Step 5: Develop a Sampling Plan ................................................................................. 82
Step 6: Purchase Equipment ........................................................................................ 82
Step 7: Install Equipment .............................................................................................. 82
Page
Step 8: Collect Calibration Data .................................................................................... 83
Step 9: Collect Count Data ........................................................................................... 84
Step 10: Estimate Use .................................................................................................. 85
System C: Mechanical Counters With Observer Calibration and Sample Interviews ...... 90
System Description .......................................................................................................... 90
Operational Procedures ................................................................................................... 90
Step 1: Decide on Use Characteristics to Measure ...................................................... 90
Step 2: Decide on Counter Type .................................................................................. 91
Step 3: Decide on the Number of Counters Needed .................................................... 92
Step 4: Develop a Sampling Plan ................................................................................. 92
Step 5: Purchase Equipment ........................................................................................ 92
Step 6: Install Equipment .............................................................................................. 92
Step 7: Collect Counter Data ........................................................................................ 93
Step 8: Select and Train the Interview Team ................................................................ 93
Step 9: Collect Calibration and Interview Data ............................................................. 94
Step 10: Estimate Use .................................................................................................. 96
System D: Visitor Registration System With Checks For Registration Rate .................. 101
System Description ........................................................................................................ 101
Operational Procedures ................................................................................................. 101
Step 1: Decide on Use Characteristics to Measure .................................................... 101
Step 2: Decide on Registration Form .......................................................................... 102
Step 3: Decide on Number of Registration Stations ................................................... 102
Step 4: Decide on Method of Estimating Registration Rates ...................................... 102
Step 5: Develop a Sampling Plan ............................................................................... 103
Step 6: Purchase Equipment ...................................................................................... 103
Step 7: Construct the Registration Stations ................................................................ 103
Step 8: Install Equipment ............................................................................................ 104
Step 9: Collect Registration Data ................................................................................ 105
Step 10: Obtain Registration Rate Data ..................................................................... 105
Step 11: Estimate Use ................................................................................................ 106
System E: Visitor Registration System With Registration Rate Checks and
Sample Interviews ................................................................................................... 110
System Description ........................................................................................................ 110
Operational Procedures ................................................................................................. 110
Step 1: Decide on Use Characteristics to Measure .................................................... 110
Step 2: Decide on Registration Form .......................................................................... 111
Step 3: Decide on Number of Registration Stations ................................................... 111
Step 4: Develop Sampling Plan .................................................................................. 111
Step 5: Construct the Registration Stations ................................................................ 113
Step 6: Install Registration Stations ............................................................................ 114
Step 7: Select and Train the Interview Team. ............................................................. 114
Step 8: Collect Registration Rate and Interview Data ................................................. 115
Step 9: Estimate Use .................................................................................................. 117
System F: Permit System With Compliance Checks ..................................................... 121
System Description ........................................................................................................ 121
Operational Procedures ................................................................................................. 121
Step 1: Decide on Use Characteristics ....................................................................... 121
Step 2: Decide on a Permit Form ............................................................................... 121
Step 3: Establish a Permit-Issue Procedure ............................................................... 122
Step 4: Decide on Method of Implementing Compliance Checks ............................... 123
Step 5: Purchase Equipment ...................................................................................... 124
Step 6: Estimate Use .................................................................................................. 124
System G: Permit System With Compliance Checks and Sample Interviews ............... 128
System Description ........................................................................................................ 128
Operational Procedures ................................................................................................. 128
Page
Step 1: Decide on Use Characteristics ....................................................................... 128
Step 2: Decide on a Permit Form ............................................................................... 129
Step 3: Establish a Permit-Issue Procedure ............................................................... 129
Step 4: Develop Sampling Plan .................................................................................. 130
Step 5: Purchase Equipment ...................................................................................... 132
Step 6: Select and Train the Interview Team .............................................................. 132
Step 7: Collect Compliance Rate and Interview Data ................................................. 132
Step 8: Estimate Use .................................................................................................. 134
System H: Permit System With Compliance Checks and Mailback Questionnaires ...... 138
System Description ........................................................................................................ 138
Operational Procedures ................................................................................................. 138
Step 1: Decide on Use Characteristics to Measure .................................................... 138
Step 2: Decide on a Permit Form ............................................................................... 139
Step 3: Establish a Permit-Issue Procedure ............................................................... 139
Step 4: Develop the Mailback Questionnaire .............................................................. 140
Step 5: Develop Sampling Plan for Survey ................................................................. 144
Step 6: Purchase Equipment and Supplies ................................................................ 144
Step 7: Obtain Mailback Responses ........................................................................... 144
Step 8: Estimate Response Rates, Compliance Rates, and Use ............................... 145
System I: Indirect Counts ............................................................................................... 150
System Description ........................................................................................................ 150
Operational Procedures ................................................................................................. 150
Step 1: Decide on Use Characteristics ....................................................................... 150
Step 2: Select the Appropriate Predictor Variable ...................................................... 151
Step 3: Select a Direct Counting Method .................................................................... 151
Step 4: Develop a Sampling Plan for Direct Counting ................................................ 151
Step 5: Install Equipment for Indirect Counts (If Applicable) ...................................... 152
Step 6: Collect Direct Count Data ............................................................................... 152
Step 7: Collect Predictor Variable Data ...................................................................... 155
Step 8: Estimate Use .................................................................................................. 156
System J: General Visitor Surveys ................................................................................. 157
System Description ........................................................................................................ 157
Operational Procedures ................................................................................................. 157
Step 1: Decide on Use Characteristics to Measure .................................................... 157
Step 2: Decide on Survey Method .............................................................................. 157
Step 3: Formulate the Survey ..................................................................................... 158
Step 4: Select and Train the Interview Team .............................................................. 162
Step 5: Develop a Sampling Plan ............................................................................... 163
Step 6: Purchase Supplies ......................................................................................... 163
Step 7: Collect Interview or Questionnaire Data ......................................................... 163
Step 8: Obtain Mailback Responses ........................................................................... 164
Step 9: Estimate Use .................................................................................................. 164
Appendices ................................................................................................................... 171
Appendix A: References ................................................................................................ 173
Appendix B: Data and Data Analysis ............................................................................. 175
Variables ........................................................................................................................ 175
Populations and Samples .............................................................................................. 175
Descriptive Statistics: Data Plots ................................................................................... 176
Stem-and-leaf Displays ............................................................................................... 176
Histograms and Bar Charts ........................................................................................ 177
Scatterplots ................................................................................................................. 179
Time Plots ................................................................................................................... 179
Descriptive Statistics: Continuous Data ......................................................................... 180
Measures of Central Tendency ................................................................................... 180
Measures of Variability ............................................................................................... 181
Page
Descriptive Statistics: Categorical Data ......................................................................... 184
Binomial Data ............................................................................................................. 184
Multinomial Data ......................................................................................................... 185
Differences Between Variables ...................................................................................... 186
One-Sample Tests ...................................................................................................... 187
Comparing Two Samples ........................................................................................... 188
Comparing More Than Two Samples ......................................................................... 189
Association of Two Variables ......................................................................................... 193
Regression .................................................................................................................. 193
Correlation .................................................................................................................. 196
Calibration ................................................................................................................... 196
Wilderness Recreation Use
Estimation: A Handbook of
Methods and Systems
Alan E. Watson
David N. Cole
David L. Turner
Penny S. Reynolds
Introduction ______________________________________________________
As stipulated by the Wilderness Act of 1964 (PL 88-577), the National
Wilderness Preservation System (NWPS) is established “…to secure for the
American people of present and future generations the benefits of an
enduring resource of wilderness.” This legislation now applies to more than
625 separate areas in 44 states, comprising nearly 105 million acres.
The goal of the Act may be stated briefly as the mandate to manage
wilderness areas so as to leave them unimpaired for future use and enjoyment as wilderness. Each individual area is to be managed to maintain
natural conditions and provide opportunities for “solitude” or “primitive and
unconfined” recreation experiences. However, it is apparent that these two
responsibilities of management may become contradictory: to maintain or
minimize loss of ecological integrity (and ensure quality solitude experiences), while simultaneously providing access for human use and enjoyment
for unconfined experiences.
Although human use is part of the wilderness mandate, human use
nevertheless results in unavoidable impact on the resource. Even at low use
levels, visitors cause substantial disturbance, both to the wilderness resource itself, and to the wilderness experiences of others. Because recreational use of wilderness continues to increase (Cole 1996), the potential for
disturbance and wilderness degradation is very great. It follows that:
(1) the management of wilderness visitors is a priority, and
(2) in order to make effective management decisions, the manager must
have reliable information about visitor use of wilderness (Watson 1990).
Monitoring wilderness status is mandated in the Act, with the primary
goals being to (1) improve wilderness management, (2) improve the acquisition and use of knowledge from wilderness, and (3) improve assessment of
status and trends. Managers must monitor wilderness use through a systematic description. In general, use measurement has two aspects: first, the
inventory of human uses that provide a baseline for planning and management, and second, a means of determining how human use and resource
conditions of the wilderness are changing. Evaluation of standards may be
performed by cataloging real and potential threats to the resource, and by
monitoring trends in condition and changes in demand and use (Landres and
others 1994). At the same time, management techniques must not detract
from “primitive and unconfined” types of experience (Cole 1995). Therefore,
empirical studies are required for both deciding upon, and verifying, the most
effective management techniques for (1) resolving a given management
problem, and (2) reducing visitor burden.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
1
The Problem: Inadequate Wilderness Use Data
Unfortunately, wilderness use has been, and continues to be, inadequately
measured and described. A recent survey of wilderness managers (comprising
423 out of a total of 440 wilderness areas) reported that 63 percent relied on
“best guesses” to estimate visitor use. Only 16 percent reported that they used
any sort of systematic procedure for determining amount of use; an additional
22 percent reported that they made estimates based on “frequent field
observation” (McClaran and Cole 1993).
There are several reasons why wilderness use is not assessed adequately:
1. Difficulty in quantifying and measuring wilderness use. Lack of funding
is the most common problem facing managers. Apart from financial considerations, logistic problems result from the size of the area, number of access
points and relative ease of accessibility, the amount of visitor use (for
example, low numbers are difficult to detect), the type of visitor use, and the
amount of resources (personnel, time) available to monitor use.
2. Little or no coordination across wilderness areas. NWPS comprises
extremely diverse units, that vary in ecosytem type, geographical location,
unit size, use, and perceived benefits. Furthermore, administration is divided
among four different federal agencies: the Forest Service in the Department
of Agriculture, and the National Park Service, Bureau of Land Management,
and the Fish and Wildlife Service in the Department of The Interior. As a
result, there is a lack of unanimity in purpose; perceived management goals
will differ widely between units.
3. Lack of quantitative and practical skills. Managers have no training on
techniques and processes available for collecting and analyzing data.
4. Lack of decision-making and judgment skills. Employment of any given
technique requires that the manager decide between competing restrictions
and priorities with respect to study objectives, desired level of accuracy,
availability of personnel, time commitment, acceptable visitor burden, and
cost. Managers may lack knowledge of the various options available for the
most appropriate and cost-effective techniques.
With little or no reliable wilderness use information, managers cannot
adequately judge resource condition trends. Visitor opinions alone are inadequate for evaluation purposes; there may be little agreement between visitor
perceptions and the actual condition of the resource, or even on the conditions
that determine “primitive and unconfined” experiences. Quality wilderness
use information is absolutely essential for examining and testing the various
tenets, principles, and dogmas of wilderness management; for optimal management of the resource, it is critical to distinguish management principles
which have been empirically verified from those which have never been
tested, and are based on nothing more than “authoritative opinions” (Cole
1995).
What is a Wilderness Use Estimation System?
To many managers, a use estimation “system” is nothing more than some
kind of measurement technique: a mechanical counter, a permit, or a selfregistration station. Measurement techniques alone do not constitute a use
estimation system. Instead, a use estimation “system” is a conceptual structure, comprising five essential steps:
2
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
1. A statement of objectives.
2. Identification of the specific use characteristics to be measured.
3. Choice of appropriate wilderness visitor use measurement techniques.
4. Choice of the appropriate strategy for sampling.
5. Choice of a specific technique and/or procedure for data analysis and
summary.
If any of these elements is missing from the system, the exercise of data
collection is of little or no value. Given the investment in data collection, it
is important to derive the maximum value from the data, and to avoid
inappropriate analyses which will generate misleading conclusions. Reliable
and high-quality data (“good” data) are obtained, not only by the type of
information collected, but also by the relevance of that information to the
study objectives, and the accuracy of the techniques used in data collection.
Handbook Organization ____________________________________________
This report is specifically designed as a convenient resource for wilderness
managers and others who have the responsibility of monitoring and describing visitor use in wilderness areas. It also should be more broadly of value to
any manager or planner trying to monitor human use of any type of
nonroaded, nonmotorized protected areas. It is a comprehensive manual on
estimation techniques and procedures that are essential to appropriately
and accurately measure visitor use-related characteristics and conditions.
Guidelines are presented that enable the manager to evaluate options and
decide on a use estimation system that meets the needs of a specific area and
set of circumstances.
This handbook is divided into two organizational units. Part I: Elements
of a Use Estimation System, consists of three chapters introducing the
fundamental components of a use estimation system. These chapters provide
the basic information necessary to adequately and reliably describe visitor
use. Chapter 1: Visitor Use Characteristics, details the types of visitor
use data that can be measured, together with methods of reporting such data
and specific areas of application. Because the selection of use characteristics
to be measured must be determined a priori in accordance with the goals of
the study, we present general guidelines for formulating study objectives. In
Chapter 2: Visitor Use Estimation Techniques, we describe specific
measurement techniques and equipment used in data collection. Also specified are the types of visitor use information that can be obtained with each
technique, estimates of relative accuracy, visitor burden, and associated
management costs. Chapter 3: Sampling Strategies, describes practical
and systematic methods of developing statistically based and field-oriented
strategies of data collection. Specific statistical methods required for elementary data analysis are included in the appendix section.
Part II: Selecting and Building a Use Estimation System, presents
the basic criteria for the evaluation, design, and step-by-step implementation of 10 major use estimation systems. The information presented in each
section should enable the reader to quickly evaluate each system in the
context of management objectives set on a case-by-case basis.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
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4
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Part I: Elements of a Use
Estimation System
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
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6
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Chapter 1: Visitor Use
Characteristics
The two aspects to the initial formulation of a use estimation system are:
1. The statement of objectives
2. Identification of the specific use characteristics to be measured
Objectives _______________________________________________________
The statement of objectives is a justification or outline of the reasons for
collecting a specific set of information; in other words, why wilderness use
measurement and monitoring are to be performed. A clearly defined objectives statement directs the entire course of the project by determining both
the type of information that needs to be collected and the purpose for which
it is collected. However, all phases of the objectives statement may be
progressively updated and revised as the planning process continues.
It is important to emphasize that the objective is not accumulation of use
information for its own sake; nor are objectives defined in terms of methods,
numerical goals or quotas, or specific measurement techniques. Instead, a
statement of objectives involves the identification of a specific wilderness
management “problem” in terms that allow some assurance of its solution
(Ackoff 1953); the collection of visitor use data will be essential to resolving
the identified problem. A management “problem” exists where there are one
or more desired objectives.
The objectives statement consists of six components (Ackoff 1953):
1. Potential participants
2. Their respective goals
3. Prioritization of the respective goals
4. Alternatives
5. Practical applications
6. The scope of inference of the intended study
1. Participants.—These involve all individuals or groups associated with
a particular use problem. At the very least, these will include the manager
and the various types of wilderness visitors. Participants outside this
immediate loop include the relevant agency, special-interest groups, legislators and congressional representatives, and so on.
2. Goals.—Goals are defined in terms of some thing, some motivation, or
some end, to be attained. Goals of the wilderness manager can be summarized as: the collection of “basic” information; identification of constraints
(finances, time, labor), which may prevent or hinder data collection; and the
practical application of this information.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
7
(a) “Basic” information may be collected in response to an immediate
problem perceived by the manager, or in accordance with one or more
wilderness directives. Such directives may result from legislative mandates,
agency reporting requirements, the requirement for feasible management
objectives, or the need to associate funding levels, maintenance, and educational programs with amounts and types of clientele served (Watson 1990).
Regardless of directive origin, “basic” information conforms to one or more of
the following categories (Landres and others 1994):
(1) Descriptors. These data constitute the basic supply side of the
NWPS. Examples include the number of miles of trail, number of visitors per
day or season in a given area, and so on. In addition, “background” description data may be critical in formulating and clarifying management objectives. Background information includes such descriptors as the number and
description of major ecosystem types, the number and location of endangered
species, and specific area issues and concerns identified by managers and
various public groups.
(2) Threats. A threat is any significant potential agent of change to
the wilderness resource. Relevant information includes identification of the
specific threat, how that agent threatens wilderness attributes, the attributes under threat, specifics of impact (type, amount, and time frame),
potential areas or specific resources most susceptible to damage, long-term
versus short-term threats, and so forth
(3) Trends in condition. Monitoring of both resource condition and
use patterns over time are essential for evaluating and directing effective
wilderness management (Cole 1989; Stankey and others 1985). Unfortunately, monitoring is performed relatively rarely, although information on
some types of monitoring procedures is available (Cole 1989; McClaran and
Cole 1993).
(4) Demands and uses may be categorized as either expressed, that
is, use and use applications that are actually performed, or latent, those uses
that are desired but not achieved. This information is critical for predicting
patterns of use and potential impact.
(5) Societal values and benefits. Public input is important in identifying potential problems and formulating management decisions about
which impacts are potentially significant, which characteristics should be
monitored, what constitutes the limits of acceptable change, what are
appropriate management strategies, and what methods of strategy implementation should be utilized. Public involvement is critical in identifying
potential sources of conflict between managers and users, and between
different user groups (McClaran and Cole 1993).
(b) Constraints, or potential limiting factors, on the amount of information that can be collected, include finances, time, labor, and potential visitor
burden. The motivation to save time and money is almost always operative
in the selection of the methods used to collect data. The budget should be
formulated with contingency planning incorporated in the event of unexpected expenses or budget cutbacks. The potential visitor burden must also
be assessed as a constraint; the use variables to be measured must always be
selected with the goal of placing little or no burden on the visitor.
3. Prioritization.—There is no management “problem” if there are no goals
to be attained, or no alternative courses of action available. However, it is
inevitable that goals will vary from group to group. For example, the
8
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
manager’s first priority may be to protect the resource, whereas visitors,
although agreeing in principle with the concept of wilderness protection, may
nonetheless resent restrictions on their own wilderness experiences. Other
groups may be actively hostile to the entire wilderness concept, or conversely,
they may advocate wholesale wilderness protection at the expense of even
mandated recreational opportunities.
4. Alternatives.—As a consequence of competing goals, and because of
constraints on finances, time, and other resources for accomplishing the
necessary work, the various objectives will have to be prioritized. Priorities
will be partially determined by the alternative courses of action available for
attaining the objectives. Available courses of action that will be open to the
investigator will be dictated by considering the relative efficiency of each
means, as well as the specific goals to be addressed.
5. Practical Application.—How the information will be used in the context
of the study should be clearly stated and given a practical working definition.
An example of a general application statement is the manager’s wish to
“learn more about visitor preferences and expectations so that responses to
management changes can be anticipated.” “Learning more” and “anticipating visitor response” are too vague to be useful. A practical redrafting of this
objective would involve:
(a) Identifying one or more specific visitor responses.
(b) Listing the methods of evaluating response.
(c) Setting practical guidelines for identifying changes in response
(that is, some baseline level would have to be identified).
(d) Identifying what management actions could be implemented if the
response is affected.
6. Scope of Inference.—The scope of the project describes the extent to
which the results can be applied and the future implications of the results.
Identification of Visitor Use Characteristics ____________________________
Once the primary objectives of the study are clearly established, the
investigator must decide on the kinds of observations that must be made. The
use characteristics chosen must adequately characterize wilderness “use” as
defined by the study objectives.
In general, visitor use data may be either quantitative or categorical.
Strictly quantitative data are usually compiled in the form of visit counts.
Count data provide a tally, or overall census, of the number of times an
individual or a group passes a specific site during a certain time period. In
contrast, other types of visitor use data may be a combination of categorical
and quantitative information. These data describe some feature or attribute
of (1) the visit, (2) the visitor, or (3) some aggregate feature of the visit, visitor,
or both. Visit attribute data describe relevant characteristics of visits, such
as length of stay, number of people per group, and activities participated in.
Visitor attributes describe traits characterizing wilderness visitors, such
as experience, demographics, and preferences. Finally, summary use statistics describe aggregate attributes; these provide an additional perspective on total amount of use by combining characteristics of the visit with visit
counts.
In this section we describe several of the most commonly used types of
observations obtained in wilderness use measurement. Data are described in
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9
terms of their working definitions, methods of reporting, the practical
applications of specific types of data, and, when applicable, the advantages
and disadvantages of certain methods of categorization.
Visit Counts
Visit counts may be recorded as either individual visits or group visits.
Individual Visits
The individual visit count is defined as the total number of single-person
visits made by people that enter (or leave) a given area during a specified time
period, without regard for length of stay. For example, a person making a 2week trip into the area is counted as one visit, two people in a group entering
the area for a single visit are counted as two visits, and so on. Conversely, a
person camping outside the area who takes two single-day trips into the
wilderness is counted as two visits.
Reporting.—Typically, individual count data are reported on a per-area
and per-time basis. Individual visits may be tallied for portions of areas. For
example, if there is particular interest in the number of visits along a specific
trail or at a specific destination area, counts of individuals can be confined to
those sites. Similarly, individual visit data may be obtained for relatively
short time periods; for example, on a per-hour, per-weekend, or per-season
basis. Alternatively, individual count data may be combined over areas or
time periods to form aggregate counts. For example, the total number of
visits to wilderness was reported to be approximately 5 million in 1986
(Lucas 1990).
Applications.—Individual visit data are required for devising site-specific
management plans. Since management emphasis is on areas of heavy use,
and use often occurs sporadically during the year, visit counts may be
necessary only during high-use periods, such as the summer season or
holiday weekends. In areas with high day use, the measurement period may
be only in peak periods.
Individual visit totals aggregated at the regional and national level provide
a gross estimate of participation levels. Such estimates provide effective
descriptions of agency output, and are important for monitoring societal
trends and developing demand/supply comparisons. These data may be
critical in regional economic analyses where it is necessary to estimate the
total effect of visitor influx and expenditures on local economies (Cordell and
others 1992).
The individual visit count is the simplest method of obtaining quantitative
data on visitor use. No additional information is required about either the
nature of the visit or the visitor. However, because such factors as length of
stay are ignored, the amount of use occurring in an area may be underestimated.
These data should be combined with other measures of visit information.
Group Visits
A group is defined as a collection of individuals taking a wilderness trip
together. It is implicit in this definition that travel and camping are shared
to some extent by members of the party. This does not preclude separate
travel arrangements to and from the wilderness site (more than one vehicle
could have transported the group to the site, different members of the group
may have originated from different places, arrival and departure times may
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differ), nor does it imply that all members of the group will necessarily be
together the whole time in the wilderness. However, if camping, members of
the group usually share a common site, and much of the traveling time is
spent together.
A group visit count is defined as the total number of single-group visits
made by groups that enter (or leave) a given area during a specified time
period, without regard for length of stay. The working definition is essentially that of the individual count, except that the unit considered is the group
rather than the individual.
Reporting.—As with individual visit counts (see above).
Applications.—Group visit data are relevant if use is heavily oriented
toward organized groups. These data will be of particular interest to management if use-rationing is contemplated, with the objective of limiting the
number of groups allowed access. Restricting access on the basis of groups,
rather than on the basis of individuals, will be appropriate in many cases
because the number of groups is the primary influence on demand for
campsites and influences visitor perceptions of solitude (Roggenbuck and
others 1982).
Visit Attributes
Observations describing attributes of each visit may be either quantitative
(such as group size, length of stay), or qualitative (such as method of
travel, use of commercial services, types of activity, use distribution
patterns, wilderness conditions, visitor perceptions, and so forth).
Various miscellaneous concerns, such as degree of compliance with lowimpact regulations, may also be documented.
Method of Travel
Although a few wilderness areas permit motorized terrestrial and waterbased transport and aircraft landings, these are rare exceptions (Browning
and others 1989). In general, transport in wilderness areas is nonmechanized.
Hiking is by far the most common method of wilderness travel. Ski and
snowshoe travel may be included with hiking (as a form of self-propelled
transport), or documented in separate categories. In many wilderness areas,
other forms of nonmotorized transport, such as canoeing, rafting, and
horseback riding, may approach or exceed hiking. Packstock (for example,
horses, llamas, and goats) are commonly used in wilderness travel.
Reporting.—Specific categories of travel are usually reported as a percentage, or proportion, of the total number of groups or individuals surveyed. If
these data are used to develop population estimates, estimates of the sample
mean should be accompanied by the sample size and an estimate of variation—all of which can be used to express a confidence interval.
Applications.—Both the location and nature (social and physical) of impact
problems will change with major shifts in travel method. Thus, need for
adjustments in management strategies and priorities in a given area may be
acquired by documenting trends in travel methods. For example, repeated
visitor surveys in the Bob Marshall Wilderness revealed that mode of travel
had shifted from predominantly horse use prior to 1970, to predominantly
hiker use by the 1980’s (Lucas 1985).
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11
Group Size
This refers to the number of individuals in a group (or party) of visitors; as
defined above, a group includes all individuals visiting the wilderness as a
unit.
Reporting.—Group size may be treated as either a quantitative or a
categorical variable. As a quantitative variable, group size is usually reported as an average (together with some measure of variation). The most
common (mode) and maximum group sizes are also sometimes reported.
Alternatively, the data set can be partitioned into several group-size classes;
the number of observations in each size class can be used to calculate the
relative proportion of groups in each class. For example, a study of visitors
entering the Bob Marshall Wilderness in 1982 reported a mean group size of
4.7; 61 percent of all groups consisted of two to four people, while only 8
percent comprised more than 10 people (Lucas 1985).
Applications.—Group size data are important for evaluating impact on
wilderness areas, and for the planning, implementation, and assessment of
management strategies for specific groups and types of activities. Information about maximum group size may be valuable in determining if facilities
can accommodate the largest groups. For example, groups travelling with
recreational packstock are generally larger than hiking groups (Watson and
others 1993). Restrictions applying specifically to packstock use may be
necessary because of trail degradation and erosion, and conflict with other
users. Many wilderness areas do not offer sufficient grazing to accommodate
“large” numbers of stock. Thus, reliable information is required to set
reasonable limits to packstock access.
Use of Commercial Services
This information indicates whether the services of an outfitter were used
on the trip and the nature of services provided. Types of service provided vary
greatly between commercial outfits. Many outfitters provide all-inclusive
packages consisting of transportation, equipment, and guides. More limited
services may be provided, consisting only of shuttle service to trailheads,
transportation of gear to a base camp, equipment rentals, or guides. It is
useful to differentiate between the major categories of commercial services
prevalent in any area, and classify groups according to the type of commercial
service utilized.
Reporting.—Data may be reported as either categorical or quantitative.
Categorical information recorded includes type of commercial service provided, extent of services, target groups, major activity of target group, and so
forth. Quantitative information may be appended with categorical data—
proportion of groups utilizing various services, average group size, time of
year, length of stay. For example, hunters use outfitters more than twice as
frequently as nonhunters do; thus, much outfitter use is concentrated in the
fall. However, in other areas, and during warm-weather seasons, river-float
operators will be more prevalent.
Applications.—These data are useful for monitoring outfitter service
allocations and for evaluating the relative necessity for, and impact of,
outfitter services. In addition, these data provide a means of determining the
magnitude of visitor impact on local economies in terms of visitor expenditures, employment opportunities, and income generated (Bergstrom and
others 1990; Watson and Cordell 1990).
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Activity Participation
The types of activities visitors engage in while visiting the area are critical
for evaluating consumer use patterns, and potential impact on wilderness.
Examples are on-trail hiking, off-trail hiking, horseback riding, hunting,
fishing, mountain climbing, rock climbing, photography, nature study,
swimming and sunbathing, collecting berries or mushrooms, and spending
time in camp. Less common activities (such as cave exploration, nude
sunbathing, athletic training, and survival training, for example) may be of
sufficient magnitude and impact to warrant documentation and monitoring.
Reporting.—Data are generally presented in a combined format of qualitative and quantitative information. Subclasses may be identified by such
categories as reasons for visit and range of activities engaged in; the number
of observations in each category are used to compute proportion of visitors in
each category. For example, a survey of wilderness visitors in the Bob
Marshall and Linville Gorge Wilderness areas determined the proportion of
visitors participating in hunting and nature study. In the Bob Marshall
survey, the proportion of visitors in each category was 16 percent and 28
percent respectively; in contrast, for the Linville Gorge area, these proportions were 3 percent and 41 percent (Roggenbuck and Lucas 1987).
Applications.—Information on type of activity is important for characterizing differential effects of visitor-expenditure patterns. Specifically, economic impact analysis determines the effect of changes in final demand on
specified economies; the change in final demand is often expressed as a
change in numbers of a certain type of recreation visitor. To date, most
analyses characterize visitor “type” in terms of activities participated in. For
example, short-term users, such as those camping at developed or improved
sites and resort customers making day trips into a wilderness, exhibit
different expenditure patterns (and thus have different impacts on the local
economy) than relatively long-term users do who stay in wilderness areas for
long periods (Watson and others 1989).
Length Of Stay
Length of stay is defined as the total amount of time spent within the
wilderness area boundaries on each trip. It may be calculated by reporting
the date and hour of entrance and exit, or by reporting the total number of
time units spent in the area (hours, days, nights, and so forth).
Reporting.—Length of stay is a quantitative variable; therefore, any
convenient measure of location and variation can be calculated (mean,
median, mode, variance, and so forth). Alternatively, observations can be
partitioned into various time classes (for example: day trip, 2 to 4 days, more
than 4 days, and so forth), and proportions of visits calculated for each
category. For example, a survey of visitors to the Bob Marshall Wilderness
Complex reported a mean length of stay of 4.7 days, and 54 percent of all trips
lasted for 4 days or longer; in contrast, a survey of visitors to the Mission
Mountains Wilderness reported an average length of stay of 1.7 days, with
62 percent of all visits being day trips (Roggenbuck and Lucas 1987).
Applications.—Length of stay can be used as a crude measure of success in
attracting the public to recreation sites (Collings and Grayson 1977). Campsite demand may be assessed by calculating the proportion of visitors that
camp overnight. Relative impact may be assessed by evaluating the proportion of visitors taking long trips of a week or more versus the proportion of
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13
users making only day trips. Finally, trends in length of stay measures
indicate the need to revise or implement area management strategies.
Temporal Use Distribution
The distribution of use through time measures the extent to which “use” is
concentrated in certain seasons, certain days of the week, or during certain
times of the day. Measures of use distribution can be obtained by reporting
date and time of entry of the individual or group, then categorizing by season,
day of the week, or period of the day.
Reporting.—Use distribution may be reported as the proportion of total
visitation that occurs in each time period (for example, per season, or on
weekends as opposed to weekdays). Alternatively, patterns may be determined by plotting use data in time order.
Applications.—Understanding temporal use distribution is important for
directing management decisions concerning the placement of survey and
maintenance personnel in the field. Data on temporal use are critical in
assessing and predicting rates of deterioration, and formulating strategies to
shift use patterns in time, thus minimizing impact due to temporal crowding.
Spatial Use Distribution
The distribution of use across the area is a measure of the extent to which
it is concentrated on certain trails or destinations. The simplest and most
commonly recorded information is the entry and exit point for each visitor or
group. An alternative is specification of the primary destination for the trip.
Detailed information on internal use distribution may be obtained by
subdividing areas into zones and reporting the time spent in each zone by an
individual or group; alternatively, visitors may provide maps of trip routes
with each campsite noted.
Reporting.—Spatial distribution is reported as area-specific proportion of
total use; for example, the proportion of users in a wilderness area that enters
(or exits) at a specific trailhead. Information on destination may be used to
compute the proportion of visitors that go to particular destinations within
the wilderness.
Applications.—This information can be useful in setting management
priorities and evaluating the extent of use concentration. Educational
messages may be targeted on trailheads that account for a large proportion
of use. Use concentration problems are likely to be particularly severe where
a few trailheads account for a large proportion of total use; these trailheads
will receive priority for development and maintenance. Mapping the amount
of use for specific zones, routes, and campsites within the wilderness is useful
in devising site-specific management plans, predicting spatial distribution
patterns of impact, and anticipating the effect of changes in specific areas on
other sites.
Conditions and Visitor Perceptions
Measures of “conditions” include information on number of encounters
with groups, individuals, or packstock along trails or at campsites; amount
of litter seen; number of encounters with wildlife; and the physical condition
of trails and campsites. Relevant measures of condition will vary from area
to area.
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Reporting.—Visitor perception of conditions, and their reactions to perceived conditions, are obtained retrospectively. This is performed via visitor
surveys in which visitors are asked for their subjective assessment of
conditions. Examples include ranking conditions from “very good” to “very
poor”; evaluating numbers of encounters in terms of “too many people,”
“about the right number,” or “too few”; evaluating certain factors, such as
amounts of horse manure on trails, as a “problem” or “acceptable.”
Applications.—This information is commonly collected by researchers in
visitor surveys, but has seldom been part of use estimation systems. However, visitor opinions on current conditions, and how conditions are perceived
to be changing over time, provide valuable auxiliary information for monitoring programs. Because such information provides a good perspective on the
extent to which problems are a concern to visitors, this information can be
used to direct management priorities and strategies.
Miscellaneous Visit Characteristics
Wilderness managers can collect a wide variety of additional information
pertaining to visits; the type of information collected, its relevance, and its
priority need to be carefully considered in the context of the stated objectives
of the study. One example of interest to managers is the assessment of
compliance with low-impact recommendations. Examples of compliance
measures include: the number of groups using stoves instead of campfires,
the proportion of groups with dogs visiting the wilderness, the incidence of
off-trail travel, the proportion of groups exceeding the maximum allowable
number per party, the proportion of packstock groups that hobble or picket
stock rather than tie animals to trees, and so on.
Visitor Attributes
The behavior of wilderness visitors is influenced by the type of activity
participated in, visitor origins and background, and visitor perceptions of
wilderness and its management. The attributes of targeted visitors will
determine certain management priorities, methods of communicating management information, and the relative effectiveness of education programs.
Specific visitor attribute data of interest commonly include sociodemographic characteristics (such as age, sex, ethnicity, and education), level
and type of past experience, knowledge of wilderness conditions and
regulations, and attitudes toward and preferences for management practices and environmental conditions encountered.
Sociodemographics
These variables describe visitors in terms of age, gender, ethnicity, education, occupation, income, and place of residence.
Reporting.—Sociodemographic data are usually collected by categorizing
each individual according to classes established for each of these variables,
and reporting the resulting proportion of visitors in each class. Comparisons
can be conducted with other areas within the wilderness or with other
wilderness areas. For example, a survey of visitor occupation conducted in
the Bob Marshall Wilderness Complex showed 37 percent of visitors were
professional or technical, 18 percent were craftsmen or operators, and 11
percent were students. In contrast, a survey of the Adirondack High Peaks
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15
Wilderness showed that students comprised 43 percent of the sample
(Roggenbuck and Lucas 1987).
Applications.—Management strategies for visitor contact and assessing
relative needs will be affected by the sociodemographic profile of the various
users groups. For example, local versus distant users will require different
methods of visitor contact; relative requirements for developed campsites
close to trailheads will also vary according to the proportion of nonlocal users
in the user population. It has been suggested that the generally high
educational levels of wilderness users should make it relatively easy to alter
behavior through education. This may not be true for a place where a large
proportion of visitors is unusually young and/or poorly educated. Place of
residence information enables managers to target specific populations for
news releases about upcoming management changes, educational programs,
or public meetings. A more general application is the economic assessment
of visitor contribution to the local economy. Economic assessments usually
exclude visitors who live inside the economic region of interest; expenditures
by “outsiders” are evaluated in the context of, for example, location of trip
expenditures, the distance traveled from place of residence to the recreation
site, and the geographic boundaries of the economic region (Bergstrom and
others 1990).
Past Experience
“Past experience” refers to the relative familiarity of the visitor with
wilderness areas and wilderness practices.
Reporting.—There has been little consensus about how to measure “past
experience.” For example, one optional question on the approved Forest
Service Visitor’s Permit (FS-2300-30) is “number of times you visited this
area in past 10 years.” Even without permit information, managers frequently categorize users as either “novice” or “highly experienced.”
Two separate domains, or classes, of experience are relevant: (1) experience
at a particular place, and (2) experience with a particular style of recreation
(Watson and Niccolucci 1992; Watson and others 1991). Within these classes,
experience may be measured in terms of length of time or frequency of visits.
The most commonly used measures of experience include:
(1) the length of time the visitor has been going to a specific wilderness area;
(2) the frequency of visits to the specific wilderness area (either the total
number of times or the typical number of times per year);
(3) the length of time the visitor has been going to any wilderness;
(4) the frequency of visits to any wilderness;
(5) the total number of wilderness areas visited.
Applications.—Visitor management strategies will differ according to user
experience. Experienced users may be more likely to exhibit appropriate lowimpact behaviors, and are therefore less in need of education or regulation.
They may also have more attachment to particular places, be more sensitive
to change, and be more tolerant of management practices involving curtailment of activities geared toward protection of the resource. More direct
management strategies may be needed with less-experienced visitors: safety
risks may be higher and high-impact behavior may be more prevalent.
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Visitor Knowledge
Visitor behavior is partially influenced by awareness of appropriate lowimpact practices, regulations, and rationale for management decisions
which may curtail visitor use. Knowledge does not necessarily translate into
practice; lack of compliance may be due to inappropriate behavior rather
than ignorance of appropriate behavior. Inappropriate behavior in defiance
of either regulations or expectations of appropriate behavior may stem from
lack of support for certain management directives. As a result, level of
support for potentially unpopular wilderness uses and practices must also be
assessed (Manfredo and others 1990)
Reporting.—Visitor knowledge may be assessed by questionnaires or
interviews. Visitors are questioned as to their awareness of (1) appropriate
low-impact practices, (2) regulations for the given wilderness area, and/or (3)
rationale for potentially controversial management decisions. Measures of
tolerance or level of support for certain practices or mandates is obtained by
asking visitors for their subjective assessment of each issue and ranking level
of tolerance (for example, “problem” versus “acceptable”; “do not support,”
“indifferent,” “strongly support”).
Applications.— Where levels of knowledge are low, it may be important to
increase education. The success of educational programs can be assessed by
periodic evaluations of visitor knowledge of appropriate low-impact practices
or regulations in the area. Knowledge of, and level of support for, appropriate
but unpopular management mandates (for example, domestic livestock
grazing, permitting certain fires to burn) are likewise important to assess on
a regular basis (Manfredo and others 1990).
Visitor Attitudes and Preferences
“Attitude” and “preference” information is a means of assessing (1) the
qualities and characteristics of the wilderness experience important to the
visitor, (2) how these expectations are met in practice, (3) current levels of
“satisfaction,” (4) “satisfaction” in comparison with previous visits to the
wilderness area or visits to other areas, and (5) perceived “defects” or causes
of dissatisfaction. Topics for assessment include both conditions encountered
in a specific wilderness setting and opinions on management.
Reporting.—Visitor attitudes and preferences may be assessed by questionnaires or interviews. There are three aspects to attitude/preference
information: (1) definition of the characteristic to be measured, (2) specification of alternatives, and (3) conflicts.
It is critical that intangibles such as “attitudes” and “preferences” are given
a concrete working definition in terms of a number of measurable attributes.
This will be accomplished within the context of the stated objectives of the
study. For example, visitors may place a high premium on the “quality” of a
wilderness experience. However, “quality” may be defined in a number of
ways. For example, “quality” may be expressed in terms of “solitude” (for
example, number of encounters per trip, number of groups camping within
sight or sound, visibility of lights originating from outside the wilderness
area), “lack of observed habitat degradation” (for example, number of
encounters with wildlife, amount of litter seen, perception of trampling
damage), “provision” of certain goods and services (for example, number of
designated campsites, number of stock corrals). Alternative attitudes and
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17
preferences may be expressed negatively in terms of characteristics which
create dissatisfaction or are perceived as defects. Finally, a number of visitor
preferences and attitudes will likely conflict. Within a particular user group
certain characteristics may rank as desirable, whereas others will rank low;
for example, a wilderness area may be excellent from the standpoint of
“facilities” provided, but rank low from the standpoint of various measures
of solitude. Conflicting attitudes and preferences may exist between user
groups; for example, hikers may be relatively tolerant of llama users,
whereas horse users may not.
Applications.—Knowledge about attitudes and preferences gives valuable
information on both the motivation of the visitor and on possible courses of
action for management. These data can be used as valuable input to selection
of indicators and standards for conditions (Lucas and Stankey 1985). This
information can be used to design quality recreation experiences and to
identify and either avoid or predict response to management actions.
Summary-Use Statistics
Frequently, measures of visitor use are reported as a combination of
several different use measures, forming a new, aggregate variable.
Visitors
This refers to the total number of people that visit an area during some unit
of time, usually a year. One person would be recorded as one visitor,
regardless of how many times he or she visited the area during the year.
Reporting.—This index is difficult to calculate. A crude measure is the
count of all visits to the defined area, summed over the period of time of
interest. Alternatively, the total number of visitors to an area may be
estimated as the ratio of the total number of individual visits to the estimated
mean frequency of visits, if this information is available.
Applications.—This index is used as a measure of the proportion of either
a particular population, or of society in general, that derives recreational
benefits from a wilderness.
Visitor-Day
A visitor-day is defined as one 24-hour day spent by one visitor at a given
site.
Reporting.—A visitor-day is calculated as the product of the number of
visits and length of stay (in days); in effect, the visit count is weighted by the
time involved. If group counts are obtained, the visitor-day index can be
obtained if information on group size is available.
Applications.—To determine use by specific categories of interest, total
visitor-days may be categorized by user type, method of travel, activity, and
so on. This requires data on the proportion of time spent engaged in each
activity, as well as length of stay.
Visitor-Hours
This is calculated in a manner similar to visitor-days, in that 1 visitor-hour
is defined as 1 hour of recreation at the site. Thus, one person spending 12
hours onsite is recorded as having spent 12 visitor-hours, a two-person group
spending 1 hour at the area would be described as 2 visitor-hours, and so on.
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This index is not in common use. If length of stay can be measured to the
nearest hour, it may be a more accurate measure than visitor-days.
Overnight Stays
One overnight stay is defined as the presence of one visitor over one night.
The aggregate is the total number of nights spent by all individuals in the
area. This index is calculated as the product of the number of individual visits
and the number of nights spent during each visit. Day use does not contribute
to the calculation of overnight stays.
Reporting.—Calculation of this index is affected by the measurement
technique used to collect the data. If a mechanical counter or observer is used
to record individual visits, the resulting estimate of total visits is multiplied
by an estimate of the mean length of stay, expressed in number of nights.
(Day users are recorded as having stayed zero nights). If visits are recorded
by means of registration stations or permits, the number of nights per visit
may be obtained simultaneously. If each individual visit is recorded, the
aggregate measure is obtained by summing the data. If group data are
obtained, group size is multiplied by the number of nights the group stayed;
the resulting value is summed for all groups.
Applications.—This is the standard unit for backcountry and wilderness
use in the National Park Service. Information on overnight stays can be used
as a measure of campsite impact and usage. However, the proportion of day
excursions are common in many wilderness areas, and vary in frequency
between areas; thus the overnight stay may be an incomplete measure of
total use.
Recreation Visitor-Days
A recreation visitor-day is defined as 12 hours of recreation at the site. One
visitor-day can be one person inside a wilderness for 12 hours, or two persons
present for 6 hours, and so on.
Reporting.—As with overnight stays, both a measure of number of individual visits and a measure of length of stay are required. If mechanical
counters or observers are used, the number of individual visits is multiplied
by mean length of stay (expressed in 12-hour units). Alternatively, the mean
length of stay (in hours) is multiplied by the number of individual visits and
the product divided by 12 to get total recreation visitor-days. Where data are
recorded on registers or with permits, the number of visitor-days is recorded
for each trip and summed.
Recreation visitor-day measures may be combined with other visit characteristics. Examples include reporting the number of recreation visitor-days
by transportation method (for example, horse users or hikers), activity
categories (for example, hunting, skiing, or hiking), and type of commercial
service used (for example, fully outfitted trips, drop trips).
Applications.—This is the standard unit used by the Forest Service for all
types of recreational use. This index accounts for both day and overnight use,
and is therefore one of the better measures for comparing total amounts of
use.
A major source of inaccuracy is the difficulty of assessing lengths of stay
shorter than 12 hours. Where day use is common, estimates of visitor-days
may be highly inaccurate unless some means of reporting or estimating
length of stay (in hours) is built into the system.
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19
Chapter 2: Visitor Use
Estimation Techniques
After it has been decided what data are to be collected, the manager must
select a specific measurement technique and/or device for collecting those
data. The most appropriate data collection technique is one that is capable of
providing the data required with a sufficient level of accuracy while maintaining both management costs and visitor burden at acceptable levels.
This section discusses various techniques available for the systematic
collection of wilderness use data. A summary of use estimation techniques
and range of application are given in table 1. Nonsystematic techniques and
methods based primarily on guesswork are not included. Each technique is
described in terms of (1) specific methods and equipment required, (2)
visitor use characteristics (the type of data) that can be obtained, (3)
visitor burden, (4) management costs associated with equipment purchase and setup, and data collection, and (5) accuracy. Comments are
added as applicable.
External Visual Observations ________________________________________
Methods.—This technique involves the visual observation of individuals or
groups outside the wilderness area; that is, as they enter or leave. Human
observers can be stationed at, or close to, trailheads to observe visitors and
record visitor use characteristics required by the study. Direct observation is
most feasible for an area with (1) a small number of access points which
account for a large proportion of total use, or (2) a program in which visitors
are regularly contacted by agency or volunteer personnel at access points.
Indirect observation methods include movie cameras or video recorders
Table 1—Summary of visitor use estimation techniques.
Technique
External visual observation
Stationary internal observation
Roaming internal observation
Mechanical counters
Registration
Permits
Surveys
Indirect estimation
Aerial surveys
Use characteristics
a
1235
12356
12356
1, 6
All
All
All
1, 5
1, 2?, 3?, 5?, 6?
Visitor burden
None
None
None
None
Low
Moderate to high
Moderate
High → low
High
Management costs
High
Variable
Low
High
Moderate
Variable
High
High → low
High
Accuracy
Variable
Variable
Low
High
Variable
High
Variable
Variable
?
a
Specific use characteristics are indicated as follows: 1 = Individual/group counts; 2 = Group size; 3 = Method of travel; 4 = Length of stay;
5 = Activity type; 6 = Use patterns; 7 = Nonobservable characteristics (sociodemographics, attitudes, experience, etc.); ? = Unknown
20
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
(modified to expose one frame at a time), or single lens reflex cameras
modified to shoot one frame either at pre-set intervals or when triggered by
visitor traffic. A mechanical counter may be used to signal visitor presence.
Observations are recorded by viewing the film in the office at a later date. An
example of a typical data sheet for reporting observations obtained from
either direct or indirect observations is shown in figure 1.
Systematic observations should be directed by a formal sampling plan.
Sampling may be randomized across access points; alternatively, stratified
sampling plans may be used, with strata consisting of access points or specific
time periods (for example, weekday/weekend or holiday/nonholiday). Care
must be taken to assure coverage of visitors entering (or leaving) in the very
early or late hours of the day.
Visitor Use Characteristics.—Data obtained by this method can include
the number of individual or group visits, group size, method of travel, location
of entry or exit, and date of entry or exit. Gender and age estimates may
occasionally be determined, but individuals may not always be distinguishable. Likewise, although day and overnight users can be distinguished by the
amount of gear carried, it is generally not possible to determine length of
stay.
Visitor Burden.—None. Visitors are not contacted, and may not be aware
that they are being observed.
Management Costs.—Relatively high. Substantial personnel time is required, regardless of whether cameras or human observers are used to
monitor visitor traffic. When human observers are used, the primary costs
are personnel time, wages, and transportation. Costs can be reduced somewhat if volunteer labor is available, or if personnel are able to combine
observations with other tasks in the vicinity of observation points. When
cameras are used, costs include equipment (cameras, traffic counters, batteries, a film editor, film), film processing, personnel and transportation costs
associated with locating, maintaining, and periodically moving the equipment, and costs associated with film viewing.
Accuracy.—Variable. Considerable sampling effort is required for even
modest levels of accuracy (Roggenbuck and Lucas 1987). Accuracy is reduced
if sampling intensity is low, the sampling plan is poor, or if there is no
commitment to following the plan. Because data obtained from human
observers are highly accurate, human observers are the preferred method of
data collection. Large variation in response and equipment failure reduces
the accuracy of mechanical counters; if mechanical counters are used, data
collected from human observers should always be used to assess the accuracy
of mechanical counters. Nonsystematic methods for obtaining observations
are used frequently; however, unknown sources of bias associated with
haphazard data collection result in data of dubious or no value.
Comments.—Possibly because of the expense involved, systematic visual
observation is not in common use. Nonsystematic visual observations are
used frequently; however, nonsystematic methods result in worthless data.
The most common mechanized method in use is a video- or camera-based
system triggered by a traffic counter. Limitations include high rates of
maintenance (for example, 35-mm cameras can provide a maximum of only
36 exposures per roll of film, thus requiring frequent visits to replace film),
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
21
WILDERNESS AREA
VISUAL OBSERVATION DATA SHEET
Date _______________________________________
Weather ________________________________________
Sample time _________________________________
Location ________________________________________
Observer ____________________________________
(Example of Observable Visitor Characteristics)
Age (approx.)
Group Group
size
Time
Entera
or day useb
Mode of
travelc
1 _____
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2 _____
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3 _____
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4 _____
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5 _____
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6 _____
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7 _____
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8 _____
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9 _____
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10 _____
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11 _____
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12 _____
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13 _____
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14 _____
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20 _____
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#
Exit/
Overnight
<=
17-
31-
46-
Over
# dogs
16
30
45
55
55
____________________
a1 = Exit, 2 = Enter
b0 = Unsure, 1 = Day use, 2 = Overnight
c1 = Foot travel, 2 = Horse, 3 = Hike with packstock, 4 = Water craft
Figure 1—Sample data recording sheet for observable visitor characteristics.
22
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
equipment obsolescence (for example, obtaining, developing, and viewing
film for 8-mm movie cameras is an increasing problem), and expense.
There are ethical, and sometimes legal, concerns about using cameras to
observe visitors. Privacy can be safeguarded by (1) adjusting distance or focus
so that individuals cannot be identified, and (2) destroying the film after
observations are recorded. In Canada there is a legal requirement to post a
notice that observation monitoring activities are occurring. Only public areas
through which visitors pass should be filmed, not campsites or swimming
areas (Lucas and Kovalicky 1981).
Internal Visual Observations: Stationary ______________________________
Methods.—Observations are taken only at specific locations within the
wilderness area. For example, if the objective is to assess visitor use along a
particular trail segment, or at a particular destination, cameras or human
observers are installed along the specific trail segment or at all entrances to
the destination area.
Visitor Use Characteristics.—Data include the number of individual or
group visits, group size, method of travel, and date of entry or exit. Additional
information such as gender and approximate age may be determined, but
individuals are not always distinguishable. Summary visitor use statistics,
such as overnight stays and recreation visitor-days, can be compiled for
destination areas. Examples of spatial use-pattern information that can be
obtained are (1) order in which available campsites are selected, and (2) use
intensity at specific target areas at destination sites (such as lakeshores).
Visitor Burden.—None. Privacy concerns must be considered because
observations are made at places where people expect privacy. When cameras
are used, they should be slightly out of focus and the film should be destroyed
after information is recorded.
Management Costs.—Variable. Costs may be relatively high if there are a
number of remote locations to be monitored; substantial transportation costs
are associated with maintaining cameras or observers in a number of remote
locations. However, if only a few sites are to be monitored, or sites are close
and popular, total costs may be relatively low. Use of observers is likely to be
more cost-effective than use of cameras; systematic observations by employees or volunteers located at a popular destination may add little additional
cost beyond normal operations.
Accuracy.—Variable. As with external observations, accuracy depends on
the adequacy of sampling. Although nonsystematic observations are commonly made, data collected haphazardly are biased, and therefore are of little
or no value. Mechanical equipment, such as cameras, are liable to failure;
equipment must be maintained, checked, and calibrated at regular intervals.
Comments.—Internal visual observation with human observers is in
relatively common use. If use is to be estimated for a few popular destinations, and personnel have other things to do, this technique can provide costeffective results. However, if visitors are relatively uncommon, observer
boredom and fatigue can be a problem; as a result, there may be no
consistency in sampling, or observers may fail to adhere to the study plan
after a time. Mechanical equipment, such as cameras, are liable to failure;
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
23
equipment purchase and setup can become prohibitively costly if more than
a few places need to be observed.
Internal Visual Observation: Roaming_________________________________
Method.—Visitors are observed during wilderness ranger patrols; patrols
are commonly scheduled for times or areas known to have heavy use.
Visitor Use Characteristics.—As above. The most useful application is to
obtain estimates of the number of overnight stays, tabulated by trail section
or destination area within the wilderness.
Visitor Burden.—None. Visitors are not contacted, and may not be aware
that they are being observed.
Management Costs.—Low. Data are collected during routine wilderness
ranger patrols.
Accuracy.—Low. Because scheduling is not random, but deliberately
selected to coincide with periods of heaviest use, this type of counting results
in highly biased measures of visitor use. Lucas and Oltman (1971) cautioned
that the “roaming technique” cannot yield a definable probability sample.
This is because the probability of any person being contacted depends on
where the observer travels, and these probabilities will generally be unknown to the observers. For example, if the observer is deep in the wilderness, there is zero probability of counting people who make short trips; the
probability of counting people who hike off trails is proportional to the
amount of time the observer spends offtrail; the probability that a user will
be enumerated is directly proportional to the length of time spent in a given
area, and so on. A reasonably accurate visitor count can be obtained if ranger
movement occurs in the reverse direction of anticipated traffic flow (Schreuder
and others 1975); however, such planning is generally impossible for wilderness areas.
Comments.—Techniques and strategies for observing visitors as an observer passes through the area have never been refined and tested. The
difficulties involved with counting mobile traffic with a roaming observer are
obvious. Systematic sampling strategies must be incorporated into this
method to obtain unbiased data. Further research as to appropriate strategies is required.
Mechanical Traffic Counters_________________________________________
Methods.—The three most commonly used types of trail-traffic counters
are photoelectric, sensor-plate, and loop-type counters. Detailed information
on suppliers, specifications, options, and prices (2000) is given in table 2.
1. Photoelectric counters consist of a scanner that emits an infrared beam,
and a reflector that returns the beam to the scanner; the counter is advanced
when the beam is interrupted (active infrared detection), or if the sensor
detects body heat and motion (passive infrared). Counts, and date and time
to the minute can be recorded. Group counts can be registered if counters
have a programmable delay that can be set to avoid multiple counts from one
group. Photoelectric counters may activate cameras; cameras may be used
either to record use directly or to calibrate the mechanical counters. Timers
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Table 2—Specifications for trail traffic counters and associated equipment.
Type
Photoelectric
Supplier
Model
Specifications
Cost
Diamond Traffic Products,
Oakridge, OR
(541) 782-3903
TTC-442
Sensitivity: 110 ft
Power source: 4 D-cell batteries
Operational Lifea: 12-15 months
Counter: $399
with 35-mm camera: $1215
with video camera: $2245
Trailmaster
Lenexa,, KS
(913) 345-8555
TM-550
Weight: 12 oz.
Sensitivity: 65 ft, width 150°, height 4°.
Temperature range: –40° to +120°F.
Power source: 4 C-cell batteries
Operational life: 1000 events, 1 year
Counter: $180
Data collector: $250
Printer: $250
35-mm camera: $290
TM-700V
as above, range to 100 ft,
Activates video camera
Power source: 4 C-cell batteries
Operational life: 3-6 months
Counter: $595
video camera: $1200
weatherproof housing for
video camera: $950
TM-1000
Sensitivity: 90 ft
Temperature: –40° to +130°F
Power source: 4 C-cell batteries
Operational life: 1000 events, 30-90 days
Counter: $205
Compu-Tech Systems,
Bend, OR
(503) 389-9132
TM-1500
as above
PIR-70
Passive infrared sensor system
Size: 3" x 6"
Sensitivity: 100' x 4' x 2'
Temperature: ?
Power source: 3 AA batteries
Operational life: up to 2 years
TR-41 series
41IR
Counters
Size: 4" x 5"
Power source: 2 N-cell batteries
Operational life: up to 4 years
41
Size: 4" x 6"
Power source: 4 D-cell batteries
Operational life: up to 1 year
CALL FOR PRICES
CALL FOR PRICES
Seismic
(pressuresensitive)
Compu-tech Systems
TSP-45
Weight: 3 lbs.; 3" x 10"
Sensitivity: 100 yds.
Temperature: ?
Power source: 8 AA batteries
Operational life: up to 3 months
CALL FOR PRICES
Loop-type
Interprovincial Traffic
Services,
Surrey, BC
(604) 594-3488
ADR-1000
Weight: 2.6 kg
Sensitivity: Variable
Temperature: –40° to +60°C
Power source: 3 to 6 V rechargeable
sealed lead acid battery (solar power option)
Operational life: 40 days
Counter: CAN $1150
ADR-2000
Data collector (include PC software)
Size: 0.75 kg; 10 x 20 x 5 cm
Temperature: –20 to +50°C
Power source: 1 to 9 V alkaline battery
Collector: CAN $1095
(Price includes batteries,
RS232 connector for
downloading to a microcomputer, computer software for calculating
summary statistics,
and shipping costs).
Spare battery: CAN $235
Battery charger: CAN $150
aOperational
limit before unit must be reset, recalibrated, recharged, or resupplied.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
25
may be set to take photographs automatically at specified time intervals
during the day.
Careful site selection and proper installation are critical to ensure accurate
counts (Deland 1976). Scanners and reflectors must be mounted at about
waist level, so there must be trees or posts on each side of the trail. Scenic
overlooks or level areas at the top of steep grades should be avoided; in these
areas people tend to stop and move back and forth across the beam of the
counter, resulting in inaccurate counts. If counts of individual visitors are
desired, it is important to select a place where trail users must pass single file
and cannot detour around the counter. It may also be important to place the
counter far enough along the trail to avoid the most casual visitors—those
who do not actually travel along the trail a significant distance.
Because visitors may tamper with, vandalize, or steal counters, counters
must be concealed and secured. There must be adequate cover to conceal or
camouflage the counter and the reflector. However, counter housing also
affects relative security. Counter housing varies with manufacturer; for
example, TrailMaster counters are housed in plastic exteriors mounted with
nylon straps, whereas Diamond Traffic Products counters are contained in
heavy steel exteriors. Securing the unit to trees with screws or bolts stabilizes
the equipment on the tree trunk and makes equipment more difficult to
remove, leaving only the plastic reflector susceptible to vandalism.
2. Sensor-plate counter (seismic sensors). Pressure-sensitive sensor plates
or mats are buried in the trail; sensors are connected to the counter unit
concealed off-trail. The sensor mat is installed 6" to 8" below the ground
surface; to ensure that visitors cross in single file, the sensor is located in a
narrow portion of the trail (36" to 40" wide) in an area that is relatively flat
and free of large rocks.
The counting unit should be concealed in a location where disturbance will
be minimal. The dust cover which fits over the liquid-crystal display of the
counter may be camouflaged with dirt and plant material. Connecting wires
(available in lengths up to 50 feet) must also be buried for concealment. The
counter must be adjusted for both sensitivity and length of delay between
readings; these must be set carefully to avoid multiple counts for people,
horses, or groups. Counters may activate cameras or be connected to other
sensors if other applications are desired. Different types of seismic sensors
may be required according to the type of ground cover. For example, sensors
used to detect cross-country skiers on snowpack will have different specifications from sensors used to monitor hikers on hard-packed dirt trails.
3. Loop-type counter. This is a relatively new type of mechanical counter
which employs microprocessor technology to store data. The counter is in the
form of a large loop (approximately 8" by 48"), which is concealed under a
layer of earth or snow (or any convenient form of covering) in the center of the
trail. Impulses triggered by visitors (hikers, horses, or skiers) passing over
the loop are stored as counts in the memory unit of the device; date and time
may also be recorded. Data may be retrieved, and the counter reset, by using
a radio transmitter and receiver, or stored.
In general, counters should be located such that travel time to and from the
counting location is minimized; however, it is also important to place the
counter far enough from the trailhead to be reasonably confident that
everyone who trips the counter actually enters the wilderness area. Initial
setup for both photoelectric and sensor-plate counters takes approximately
1 hour; this includes setting the sensitivity and time-delay, and concealing
26
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Photo-electric counters emit an infrared beam, and a reflector returns the
beam to the scanner. Careful site selection and proper installation of photoelectric counters are critical to ensure accurate counts.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
27
the unit. The units are battery-powered; therefore, primary maintenance
requirements will be battery replacement, and if camera attachments are
included, units will have to be checked for mechanical failure and film
replaced at regular intervals. The equipment is lightweight, reasonably easy
to conceal, has a reasonably long operational life, and functions under a wide
range of weather conditions.
Visitor Use Characteristics.—Data obtained from mechanical counters are
restricted to individual or group counts, and the location and extent of use
during a specified time period (between counter readings). However, when
combined with visual observations, data can be obtained for group size,
method of travel, approximate length of stay (overnight versus day use) and
gender and approximate visitor age. When counters are used near trailheads,
additional information will be required to estimate distances traveled and
use patterns within the wilderness area. For example, in the Great Smoky
Mountain National Park, only 25 percent of trail users counted with a
mechanical device hiked beyond 1⁄2 mile from the parking lot on one trail,
while more than 50 percent completed an 8-mile round trip on another trail
(Burde and Daum 1988).
Visitor Burden.—None. Visitors unknowingly trip the counting mechanism when passing the counter trigger.
Management Costs.—High. Equipment requirements and costs are outlined in table 2. Associated personnel costs (wages, time, and labor) are
incurred with installation, maintenance, and calibration of the counters.
Installation time will vary by the method selected. For example, selection of
an appropriate site depends on both the nature of the counter, as well as the
need for concealment; adjusting the aim of infrared beam is tricky. A possible
option to incurring the large initial expense of equipment purchase and
installation involves cooperation with state highway transportation departments. Because these departments already possess traffic counting equipment and experience with calibration and maintenance, managers may
prefer to explore this possibility rather than duplicate equipment and
training.
The greater the number of access points that need to be monitored, the
higher the cost is going to be for equipment and maintenance. Calibration is
expensive if performed on a regular basis; to check the validity of mechanical
counters, either human observers will have to periodically observe use, or
cameras will have to be installed and film viewed. Rarely, visitors or wildlife
may damage counter equipment, necessitating equipment replacement.
Accuracy.—High. However, accuracy is high only if care is taken in installation and calibration, and routine maintenance is performed. Accuracy is
seriously compromised if battery power runs low or other mechanical failure
occurs, or if calibration procedures are neglected. The sampling effort
required will be substantial because of high variability in certain classes of
visit and visitor characteristics (for example, group size or gender); accurate
estimates of such groups will require large sample sizes.
It is extremely important that units are calibrated on a regular basis.
Counter readings are subject to many sources of inaccuracy. For example,
wildlife using the trail may not be differentiated from people; passive
infrared counters may count even small animals which are not on the trail.
Sensitivity of sensor-plate counters, if set too high or too low, will over- or
underestimate use. Therefore, readings must be validated independently.
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Counter readings can be calibrated by visual observation, either by people or
with cameras. Use of field personnel has the advantage of making it possible
to derive additional information on visitor use. Counter sensitivity and delay
may be adjusted in some cases to match counter readings with observations.
Any residual difference will have to be accounted for through correction
factors.
Most operational problems are related to improper initial setup and
installation. Most devices are resistant to false tripping when correctly
installed. However, significant counter error associated with photoelectric
sensors may occur as an indirect result of various environmental factors: for
example, wind-induced sway of the tree on which the counter or reflector was
fastened, snow and fog, and falling leaves.
Comments.—Traffic counters are used relatively frequently; however,
calibration is usually sporadic at best. This is unfortunate because unless
equipment is calibrated against a known and accurate standard, use estimates will be highly inaccurate and misleading. Traffic counters may be
much less expensive than direct observation, but costs increase greatly with
the frequency of calibration.
Because of counter bias and errors induced by mechanical failures, use
estimates obtained from counter data are usually much less accurate than
those obtained by visual observation. A less-expensive and highly efficient
strategy combining both methods could employ visual observation at highuse areas, and mechanical counters (calibrated with cameras) at low-use
areas.
Registration ______________________________________________________
Methods.—Visitors voluntarily register by filling out survey cards before
entering the area, and use characteristics are obtained from the resulting
information. Registration stations are usually unstaffed and located at, or
close to, trailheads; registration stations may also be located at staffed visitor
centers or ranger stations.
The distinguishing feature of this technique is that registration is voluntary. However, the location, design, and maintenance of registration stations
all influence the likelihood of visitor registration. Stations located a mile or
two up the trail have considerably higher registration rates than stations at
trailheads (Petersen 1985). This observation suggests that criteria for a
“good” location include lack of competing information, a reduced concern
with packing up and getting on the trail, and opportunities to stop or rest.
Places where users are likely to stop are points of interest, a scenic view, a
stream crossing, the top of a hill, terrain allowing users (especially stock) to
stop safely and easily, or an area where the station is easily seen by
approaching visitors. Registration by stock users is difficult to obtain;
targeting stock users by installing registration stations at stock-unloading
facilities may increase registration rates.
Registration rates are increased if registration stations are marked by an
attractive sign. The message on the sign should (1) clearly and simply explain
the purpose of collecting information from visitors (Petersen 1985), and (2)
provide clear instructions as to what the visitor is expected to do. Registration stations should be maintained on a regular basis, keeping them supplied
with registration cards and pencils and collecting the completed cards.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
29
Figure 2—Voluntary registration card as used in the Bob Marshall Wilderness, MT.
One variation of the registration technique is to have visitors complete
registration cards both when they enter and when they leave the area. This
system has been tested in National Park backcountry and in some Forest
Service wilderness areas. Visitors pick up two cards when they enter the
area. They are asked to fill out and leave the first card when they pass the
registration station, and to complete the second card during their visit and
deposit it when they leave the area. One variation is to affix a postage stamp
to the second card so it can be sent in from the visitor’s home, if he or she
forgets to deposit it upon exit. More visit characteristic information can be
obtained by this method than by standard registration techniques; for
example, routes of travel, points of entry and exit, social and resource
conditions encountered, and reactions to those conditions, and more accurate
estimates of length of stay. Because many trips do not last as long as
originally expected (van Wagtendonk and Benedict 1980), length of stay is
usually overestimated when data are obtained from visitors before their
trips.
The disadvantages of this technique are that (1) registration rates would
likely vary for the two cards, and both would have to be estimated, (2)
clearance by the Office of Management and Budget (OMB) of any questions
not currently approved for visitor registration must be obtained, (3) this
technique is not in sufficient use to be evaluated rigorously. However, it
offers several advantages over standard registration formats. More information can be collected than with standard registration cards, at little added
cost to visitors or to managers. It seems to be particularly useful for more
remote places when managers are interested in getting information on
conditions that visitors encounter (such as the number of people they meet)
or in their satisfaction with conditions and/or management. It is a much
30
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
cheaper method of collecting this information than by the more commonly
used visitor surveys.
Estimation of registration rates remains a challenge, particularly at
remote places. However, pilot tests using cameras to estimate registration
rates have found sufficiently high rates of registration by hikers at remote
access points to allow highly accurate estimates of use.
Visitor Use Characteristics.—The types of information that can be collected are constrained only by what can be placed on a registration form.
Currently, the Forest Service uses a card that has been approved by the
Office of Management and Budget (OMB) (fig. 2). The OMB-approved Forest
Service visitor registration form (FS-2300-32) provides information on the
number of individual and group visits, group size, method of travel, length
of stay, entry and exit locations, destinations, dates of entry and exit, and
place of residence. The number of overnight stays can be calculated and
recreation visitor-days can be estimated.
Additional information may be collected for other purposes. If visit or
visitor characteristic data are required beyond what is on the registration
form, a sample of registrants could be asked the supplemental questions.
This information, in conjunction with an estimate of registration rate, would
allow the manager to predict these additional items for the population of
registrants. For example, suppose the manager wished to determine how
many visitors had made previous visits to the area, as a means of estimating
how many novice versus how many experienced visitors the area might be
expected to accommodate each year. A sample of registrants would be
surveyed. Then, if it were determined that, for example, 20 percent of hikers
and 60 percent of stock users had made previous visits, these data can be
applied to the larger population estimate of users to obtain an estimate of
novice versus experienced visitors of each use category which enter the area.
Variations in survey cards must receive prior approval from OMB. It
should be noted that registration rates are likely to decline if too much
information is requested.
Visitor Burden.—Low. Registration is voluntary, and it takes little time to
fill out a survey card. If the station is suitably placed at a point that visitors
would naturally stop, registration is more convenient. However, associated
visitor burden is higher than for visual observation or traffic counts.
Management Costs.—Moderate. Registration stations must be constructed
and installed. Location will influence registration rates (as indicated previously) as well as the relative incidence of vandalism; stations located a ways
up the trail from the trailhead have higher registration rates and are less
prone to vandalism. However, because transportation time increases, distant stations are more costly to maintain.
Stations must be maintained on a regular basis by supplying them with
cards and pencils, and collecting completed survey cards. Data must be
compiled on a regular basis. The time commitment is probably comparable
to that involving the use of traffic counters, and is less than that associated
with visual observation. Checking registration rates requires additional
time and equipment (if cameras are used); however, time and equipment
needs are not likely to be substantially higher than that required to calibrate
traffic counters.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
31
Accuracy.—Variable. The level of accuracy depends on maintenance of the
station and the adequacy of registration rate estimates. If funding is
insufficient to keep stations supplied with cards and pencils, the resulting
data will be of dubious value. However, estimation of rates of registration is
the most critical factor in the estimation of total visitor use.
Data will not be accurate if registration rates are unknown or only crudely
estimated. Estimates of registration rates are necessary because registration is voluntary and there is no official sanction against not registering;
therefore, a large and variable proportion of visitors do not register.
Registration rates vary greatly between location (for example, rates for dayuse horseback riders range from a low of 0 percent in the Bob Marshall
Wilderness (Lucas 1983) to 89 percent in the Rawah Wilderness (Roggenbuck
and Lucas 1987)), main activity (hunters register at a lower rate than
hikers; hikers register at higher rates than horse users), length of stay
(overnight users register more frequently than day users do), party size
(large parties have higher registration rates than small parties have), place
of residence (visitors who come from far away register more often than local
people do), time of day (those arriving after 6 p.m. were less likely to register
than those arriving at other times; Leatherberry and Lime 1981), season of
visit (spring and fall visitors were less likely to register than summer
visitors), and frequency of previous use of an area (Wenger and Gregerson
1964).
Registration rates can be determined in a number of ways, including
visual observation by human observers and the use of sensor-triggered
cameras. The most common and cost-effective techniques used in recent
years is a movie camera triggered by a photoelectric counter (Roggenbuck
and Lucas 1987), or human observers stationed at high-use entrances.
Estimates of registration rates used to correct for nonregistering visitors
are called the “expansion factor.” For example, if only 50 percent of users
register, registration data will need to be doubled to obtain a representative
visitor total; therefore, the expansion factor is 2. Accuracy is greatly
increased if separate registration rates and expansion factors are calculated
for different subgroups of the population. Alternatively, if it can be assumed
that the mix of visitors using a given trail is relatively stable, registration
rates and corresponding expansion factors can be calculated for each
separate trailhead.
Comments.—Registration is relatively inexpensive and places little burden on the visitor. The major consideration is the requirement for reliable
estimates of registration rates. Although methods of estimating registration
rates are neither highly complex nor expensive, many managers fail to
commit necessary resources. As a result, much registration data collected is
of unknown accuracy, and is therefore useless for estimating wilderness use.
Permits _________________________________________________________
Methods.—Permits are use-authorization forms issued by the agency. In
many cases, the available number of permits is limited to control amount of
use in a wilderness area. Permits may be obtained from the agency office, by
mail, over the phone, in person, or may be self-issued; self-issued permits are
usually obtained at the trailhead or immediately outside agency offices.
Visitors fill out the permit, leaving a copy at the station and taking the
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original with them on their wilderness visit. General permit categories are
summarized as follows:
1. Source of issue. Permits may be self-issued or issued only by agency
personnel.
2. Restrictions on type of use. Use allowed by permits may be either limited
or unlimited.
3. Restrictions on type of user. Permits can be required for all users, only
overnight users, only overnight users during high-use times (for example,
summer weekends). Combinations are also possible. For example, the Desolation Wilderness has a limited number of agency-issued permits for overnight users, whereas there is (currently) an unlimited number of self-issued
permits available for day users.
Permit format must be approved by OMB; Forest Service-issued visitor
permits are authorized under the same OMB clearance (0596-0019) as the
registration form.
Visitor Use Characteristics.—As with registration data, the information
that can be collected is constrained by what can be placed on the permit form.
A sample OMB-approved permit is shown in figure 3. Data obtained from
permits can include number of individuals/groups, group size, method of
travel, length of stay, entry and exit locations, destinations, routes of travel,
dates of entry and exit, and place of residence. This information may be
sufficient to estimate other categories of use, such as number of overnight
Figure 3—OMB-approved mandatory permit form.
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stays and recreation visitor-days. Information on other types of visitor
characteristics, such as gender and age, can be obtained if permits are issued
at offices, or during compliance checks.
The Forest Service permit includes two optional questions which may be
completed if the permit is issued at the agency office. These are:
(A) “The number of times you visited this area in past 10 years”
(B) “Is visiting this area (1) the primary purpose of your trip away from
home, (2) one of several important things you planned to do on your trip, or
(3) something you decided to do after arriving near the area?”
The National Park Service backcountry use permit includes the same basic
information as the Forest Service visitor registration and visitor permit.
However, the Park Service requires more specific information on camping
locations; the two optional questions are not included.
Visitor Burden.—Relatively high. One component of burden may be the
perceived sense of regimentation and control implied by permits. Burden is
increased when visitors are required to visit agency offices. Office visits may
represent a logistic problem for some users; for example, groups that arrive
at trailheads after office hours will have difficulty complying with requirements to obtain an agency-issued permit. The self-issued permit will not be
as much of a problem for users if permits are made available at the trailhead;
in this case, visitor burden would not differ from that associated with
trailhead registration. However, this option can only be used where the
number of permits issued is unlimited. Alternatives which increase user
convenience include mail, telephone, and even private sector cooperators. In
general, visitor reactions to permits have been highly positive, as long as the
rationale for permit issuance is considered worthwhile (Lucas 1990).
Strategies for reducing visitor burden (Leonard and others 1980) include:
1. Publicizing requirements for permits in areas where users are known to
live or start their trips.
2. Ensuring that the potential user population is made aware of use limits
or restrictions that are enforced through the permit system.
3. Clarifying the type of use, or user, requiring a permit.
4. Minimizing (as far as possible) the amount of information required from
users.
5. Increasing the convenience in obtaining a permit.
Management Costs.—Variable. Management costs will vary greatly according to the type of permit system. For example, a system of unlimited selfissued permits is relatively inexpensive. Apart from the costs involved in
managing the registration system, additional costs are incurred by enforcement; however, these costs will be minimal if other enforcement duties and
field tasks can be performed simultaneously. In contrast, where the number
of permits are limited and demand for those permits is high, administrative
costs can be relatively expensive. (However, those costs do not result from the
use of permits as a use estimation system; they result from the use limitation
strategy). Where permits are agency-issued but unlimited, costs are moderate.
Office personnel must be available to issue permits. This might involve
directly issuing permits to visitors coming to the office, which requires a more
centralized distribution. In contrast, indirect methods may impose less
burden on both users and personnel, and less restrictions on location; these
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include mailing out permits, or posting permits outside the office after hours
for late arrivals, or providing for permit issue on the basis of telephone
requests. In some cases, outfitters are allowed to issue agency permits for
their own trips; these permit receipts need to be retrieved periodically from
outfitter offices and checked for completeness and accuracy. Field personnel
are less involved in data collection than they would be with visual observation or traffic counter systems.
Accuracy.—Usually high. Permit systems differ from registration systems
in that permits are mandatory, rather than voluntary. Visitors must obtain
a permit to enter an area, otherwise they are in violation of regulations.
Accurate estimation of use characteristics from a permit system is reduced
by lack of compliance. When permit requirements are well enforced, compliance is usually relatively high. For example, compliance in a number of
National Park wilderness areas is more than 90 percent; compliance is more
variable with self-issue day-use permits, ranging from 53 percent in one area
(Lucas and Kovalicky 1981) to as high as 80 percent in other areas. Permit
compliance increases with increased levels of enforcement, increased publicity about permit requirements, and increased visitor awareness of requirements (Lime and Lorence 1974).
The level of accuracy depends primarily on the accuracy of estimated levels
of compliance. An estimate of compliance rates is required to correct for the
unknown proportion of visitors not in compliance; this is the “expansion
factor” similar to that determined for registration data. The compliance rate
(which is identical to a registration rate) is simply the proportion of all groups
encountered that have permits. It can be estimated by checking permits,
either systematically or randomly; checks can be performed by rangers on
patrol or stationed at or near trailheads. Ranger checks are most often
performed within the limits of a normal work schedule, often at high-use
times; however, reliability of compliance estimates can be increased if checks
are assigned randomly. Because of observed differences between different
types of users (Lime and Lorence 1974), expansion factors to account for
noncompliance rates should be calculated by user subgroup (for example,
horse users versus hikers, or day-users versus campers). Accuracy may also
be compromised by visitors changing their plans after obtaining their permit.
Such changes usually result because people overestimate their abilities, or
do not account for changes in weather. For example, at Yosemite National
Park, 62 percent of all groups deviated from their planned trip; as a result,
permit data overestimated use by 12.5 percent (van Wagtendonk and
Benedict 1980). Compliance with permit requirements by visitors to Sequoia
and Kings Canyon National Parks was 97 percent; however, changes in plans
resulted in overreporting of total visitors by 8 percent, and of visitor-nights
by 23 percent (Parsons and others 1982). The validity of permit data can be
checked by contacting a sample of visitors, either as they leave the area or at
their home after the trip, and asking them about their travel behavior.
Comments.—The use of permits is controversial (Behan 1974). Most of the
controversy stems from the use of permits as part of a use-limitation system.
This is unfortunate because permits have many positive attributes that do
not have to be coupled to a use-limitation system. For example, when
compliance is high, permits are a simple method of collecting accurate use
data; a large number of visitor use statistics can be gathered. Permit issuance
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offers an opportunity for contact between visitors and agency personnel. This
can be used to increase visitor knowledge about regulations, recommended
low-impact behaviors, and potential hazards. It gives visitors a chance to
obtain information of interest to them, it increases the professional image of
the agency, and it may add an element of increased safety (Hendee and Lucas
1973).
In 1980, permit systems were in use in 69 wilderness areas. Of these areas,
17 limited use and 52 did not (Washburne and Cole 1983). Recent informal
surveys suggest that the number of wilderness areas that issue permits has
declined since that time. Approximately 50 areas currently require permits;
however, the number of areas that limit use has increased to about 25. Most
of these changes have occurred in areas managed by the Forest Service.
These findings suggest that use of permits as a tool for collecting visitor data
and communicating with the public is decreasing.
Visitor Surveys ___________________________________________________
Methods.—A visitor survey consists of two parts: (1) contacting a sample
of visitors (either at trailheads, within the wilderness, or at home); and (2)
obtaining visitor use information by either interviewing visitors or
asking them to respond to a questionnaire.
1. Visitor contact. Strategies of contacting visitors must identify the
sampling design to be used, the timing of visitor contact, and the location of
contact.
There are three principal types of sampling design used to obtain a
representative sample of visitors:
(a) Stratified samples of visitors at, or close to, trailheads.
(b) Random or systematic sampling of either permits or registration
forms, or both.
(c) Convenience sampling.
Stratified sampling involves the placement of personnel at or close to
randomly selected trailheads; the strata are time blocks selected from
available weekdays, weekends, and holiday periods. Visitors are interviewed
or asked to complete a questionnaire as they enter or leave the wilderness;
alternatively, personnel can obtain names of visitors who are then sent a
mailback questionnaire. Personnel could also ask visitors for information
regarding length of stay; this information can be used for estimating such
summary visitor use statistics as recreation visitor-days. Stratified sampling
is most efficient if observers can combine interviewing with counter validity
checks or monitoring registration rates.
Random or systematic sampling of permits may be used to obtain the names
and addresses of visitors; the visitors thus sampled are subsequently sent
mailback questionnaires. Sampling from permit lists is inexpensive. However, the information provided is usually restricted to the permit compliers,
group leaders, or whoever registers or fills out the permit. Information
regarding other party members can be obtained by asking group leaders to
supply names and addresses of party members; questionnaires may be
subsequently mailed to a sample of party members. Some wilderness areas
(for example, the Okefenokee National Wildlife Refuge Wilderness) require
the names of all members of the party on the permit.
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Visitor contact strategies for surveys must identify the sampling design to
be used, the timing of visitor contact, and the location of contact.
In theory, registration information could be used in the same manner as
permits to derive a sample of wilderness users, especially if registration rates
are known to be high. However, registration rates are much lower in general
than permit compliance rates. Examples of visitor use surveys using registration data are (1) at Cranberry Backcountry in West Virginia, where
registrants were randomly selected, and nonregistrants were systematically
selected on randomly selected days (Echelberger and Moeller 1977); (2) at the
Bob Marshall Wilderness Complex, where visitors were sampled directly at
moderate- to high-use trailheads, and registration cards were sampled at
more remote, low-use trailheads (Lucas 1985).
Convenience sampling does not provide a representative sample of the
population, because the lack of true randomness in sample selection introduces an unquantifiable amount of bias. Convenience samples may be
justified occasionally as a means of obtaining information on, for example,
visitors to a specific internal location (such as a lake basin), or noncompliers
(Lucas and Oltman 1971; Watson 1993). Sampling is performed by patrolling
rangers, or by personnel stationed at entry points to the wilderness. Personnel would then interview all the visitors encountered in that particular
location. The National Park Service, through their Visitor Service Project,
advocates what they call “taking the pulse” of visitor use with intense
convenience samples of visitors.
Other methods of contacting visitors may be required when trailheads are
not established, use is very low or follows unknown patterns, or cost-efficient
alternatives are not readily available. For example, the Corps of Engineers
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37
attempted to contact a sample of dispersed hunters by placing response cards
on vehicle windows on selected sample days; respondents were asked to
deposit completed forms in a designated roadside box. Unfortunately, this
approach provided a response rate of only 25 percent. The Forest Service,
working at Upland Island Wilderness in Texas with very dispersed and
unpredictable entry and exit patterns, contacted apparent recreation visitors by placing mailback cards on vehicle windows; response rates were
almost equally low (Watson and others 1992). In contrast, roadside traffic
surveys were used to contact visitors in a Forest Service wilderness in
Indiana, characterized by an abundance of easy access points from along
adjacent roads; visitors were contacted at places where all visitors to the area
had to pass (Watson and others 1993). Although visitor contact was highly
successful, approximately 50 percent of all vehicles stopped were not wilderness-visit-related traffic. Further consideration of alternative sampling
designs are required.
The timing of visitor contact is important. Visitors may be contacted when
either entering or leaving the area. Information obtained from visitors after
their trips is generally more useful; in addition, visitors may be more open to
questions when leaving the area. The most cost-effective method, when possible,
is to contact visitors arriving and departing during a selected time period.
The location of visitor contact must be carefully selected in order to avoid
undesirable intrusion into the wilderness experience of visitors. Surveys
conducted at trailheads are considered most acceptable. Visitors have occasionally been contacted at campsites and along trails in the wilderness, but
these locations are generally considered intrusive.
2. Obtaining information. Information is solicited from visitors by
means of interviews or questionnaires. Interviews should be kept short,
limiting content to easy-to-answer, factual questions. Whether the visitor is
either just setting out, or leaving for home, there will be low tolerance for
complicated and difficult-to-understand questions, and long, time-intensive
interviews.
The second option for collecting detailed visit and visitor characteristic
data is the mailback questionnaire. Typical response rates to questionnaires
4 to 16 pages long range between 77 percent and 85 percent (Dillman 1978).
However, this level of response usually entails diligent followup; followup
procedures include (1) provision of a postage-paid envelope with the questionnaire, (2) mailing out a reminder postcard, (3) mailing a complete second
questionnaire and return envelope 3 weeks after the first mailout, and (4) a
final mailing of a third questionnaire and return envelope after 7 weeks.
Visitor Use Characteristics.—Any type of visitor information can be
obtained.
Visitor Burden.—Moderate. The extent of visitor burden is determined by
the location and timing of visitor contacts, and the time required for each
visitor to respond to the questions on the survey.
Most visitors appear to value the chance to provide input on wilderness
issues, because these issues are important to them. This suggests that visitor
burden will be a problem (1) where visitors are contacted within the
wilderness (many visitors enjoy this contact, but some do not), or (2) if
interviews are too long, and visitors are anxious to either enter the wilderness or get home. Visitors seldom complain about mailback surveys, even
those that require as much as 30 minutes to complete.
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Management Costs.—High. Statistically valid visitor surveys are expensive. Personnel costs include transportation and time required to monitor
different trailheads; administration of the survey may require additional
field personnel. When names and addresses need to be collected in the field,
there are no great savings associated with mailback surveys. When names
can be obtained from a list of permits, however, costs are dramatically
reduced because no field contacts are needed. Costs of mailbacks include the
cost of questionnaire preparation, printing and mailing, and follow-up costs
(postage-paid envelopes, reminder postcards, and follow-up questionnaires).
Personnel time is needed to code and enter data and to analyze the results.
Convenience samples can be substantially less expensive. Data can be
collected as a part of field employees’ normal jobs, so little additional cost is
incurred. However, the quality and utility of information is substantially less
than that obtained from a valid sample.
Additional costs may be incurred by the time and effort it takes to obtain
OMB approval. Federally sponsored information collection procedures requiring individual responses must receive clearance by OMB. The approval
process requires a lead time of about 3 months from the time of submission
to approval; a substantial amount of paperwork is involved. However, the
review and justification required to obtain this clearance assures a highquality survey plan. OMB clearance is critical when important management
decisions are to be based on collected information. The clear approval and
support of the agency, the Department, and OMB will avoid later problems
concerning questions of authority and legality.
Accuracy.—Variable. The level of accuracy is largely dependent on the
sampling procedure. Statistically sound, unbiased sampling techniques
produce the most accurate information. Convenience samples do not provide
a representative sample of the population because the amount of associated
bias is unknown; the quality of the data obtained from convenience samples
is therefore low.
Comments.—Surveys are the most frequently used method of obtaining
detailed information on visitor characteristics, visitor attitudes, and visitor
preferences. The use of surveys is increasing with the current emphasis on
“knowing your customer” and maximizing “customer satisfaction.” The
survey has been used almost exclusively by researchers; however, it is a
practical technique for managers needing to collect information about
recreational use.
Indirect Estimation ________________________________________________
Methods — Indirect estimation techniques involve the prediction of some
desired visitor use characteristic from one or more easy-to-measure variables. These surrogate measures are the predictor variables. The relationship between the predictor(s) and the use measure is quantified by linear
regression. The relative “success” of the predictor variables in predicting the
use characteristic is evaluated by the R2 value calculated for the regression,
or the width of the confidence interval for the estimate of the “new” predicted
2
value. The higher the R , the more successful the regression model will be in
explaining the variation in the use characteristic. Once this relationship is
quantified, it is only necessary to monitor the predictor variable(s) to obtain
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an estimate of the desired use characteristic. Examples of such predictive
relationships are:
1. The estimation of dispersed recreation day use in Glacier National Park
from weather factors, campground occupancy rates, and the total number of
vehicles entering the Park; variation explained by the predictive model was
75 percent (McCool and others 1990).
2. The estimation of the number of people using the Kissimmee River
Basin, Florida, from lake water levels, daily maximum temperature, and
daily rainfall; variation explained by the predictive model was 69 percent
(Gibbs 1973).
3. The estimation of the number of visitors per day to a given lake basin
from systematic car counts obtained at the trailhead parking lot; variation
explained by the predictive model was 94 percent (Watson and Cronn 1999).
4. The estimation of dispersed recreation use from vehicle traffic recorder
counts placed along major access roads (Erickson and Liu 1982; James 1967;
James and Ripley 1963).
5. The estimation of fishing visitor-days from vehicle traffic counts obtained at both ends of a parking lot (James and others 1971).
An affiliated method of some promise is “double-sampling.” This involves
the simultaneous measurement of a given use variable and a suitable
predictor variable on a predetermined number of randomly selected sample
periods during the use season. Common predictor variables used in doublesampling designs are traffic counts or rates of water consumption at developed sites. Other potential predictor variables include the number of cars
parked at the trailhead or the number of trailhead brochures or maps taken
by wilderness visitors. Double-sampling is closely related to “cordon” sampling (Erickson and Liu 1982, Roggenbuck and Watson 1981, Saunders
1982); cordon sampling is a method of estimating annual recreation use by
interviewing recreational users at roadblocks situated along wilderness area
access roads.
How the predictor variables are measured obviously depends on the types
of variables chosen. For example, several studies estimated dispersed recreation use as a function of vehicle traffic recorder counts (Erickson and Liu
1982; James 1967; James and Ripley 1963). In these studies, use characteristics were determined by survey sampling of traffic along major access
roads; these surveys were coupled with vehicular counts obtained by inductive loop or pneumatic tube counters.
The predictor variables selected must be carefully evaluated, both for their
initial suitability as a predictor variable, and for their continued suitability
over seasons. For example, measures of trail deterioration, such as trail
width and condition, will be adequate predictors of trail use only if trail use
is classified simply on the basis of light versus heavy use; these predictors will
be inadequate if more rigorous predictions of trail use are required (More
1980). Furthermore, the predictive power of certain predictor variables may
be affected by both the activity being evaluated and the location of the study.
For example, the precision of various categories of predicted visitor use in the
Eldorado National Forest was described with 95 percent confidence intervals; precision ranged from ± 15.8 percent for fishing activity over the entire
forest, to ± 130.6 percent for swimming and sunbathing at one site (James
and Henley 1968).
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Some indirect relationships may be useful for long periods of time if use
patterns do not appear to change noticeably. For example, the predictive
relationships established between visitor use and traffic counts may be valid
for 3 to 5 years (Saunders 1982). However, periodic checks should be
scheduled to ensure the continued validity of the predictive relationship.
Visitor Use Characteristics.—Potentially, indirect measurements could be
used to predict many types of wilderness use characteristics. However,
certain use characteristics may not be modeled adequately by a suitable
predictor variable; this must be ascertained in preliminary, or pilot, studies.
To date, the use characteristics most commonly evaluated have been total
amount of visits, and time involved in a particular activity. Inter-party
encounter rates have been successfully predicted from a combination of
mechanical counts, visitor counts, and systematic counts of parked vehicles
(Watson and others 1999). The relative success of predicting other visit and
visitor characteristics is untested.
Visitor Burden.—Variable, but should decline to zero. During initial data
collection for establishing the predictive relationship, visitor burden will be
determined by the number and type of use statistics to be predicted, and the
method of obtaining visitor information (on-site interviews, observation,
mailed questionnaires, and so forth).
Once the predictive relationship is established, visitor burden should go to
zero, except for periodic checks required to ensure the continued validity of
the predictive relationship.
Management Costs.—Initially high, but should decline to low levels.
Considerable effort must be expended in developing the predictive relationship between the use characteristic of interest and some appropriate predictor. Accurate information must be obtained for both the use characteristic
and the selected predictive variables. Pilot studies are imperative to determine whether there is in fact a relationship between the given use characteristic and the proposed predictor variables, and whether the proposed relationship is sufficiently strong to be of any use as a means of prediction.
Initial costs would include the purchase cost of equipment required to
monitor the predictor variable and personnel costs associated with collecting
initial data. However, these costs may be incurred only over the short-term,
generally for a single year or use season. The resulting predictive relationship may be able to be used for several years with some confidence before
reevaluation of the predictive relationship is needed. Large initial expenses
may be avoided by cooperation with other agencies (borrowing or timesharing of equipment and personnel).
Accuracy.—Variable. Accuracy depends on the type of predictor variable,
and the strength of the relationship between the predictor and the use
characteristic being estimated. Tarbet and others (1982) emphasized the
need for formalized sample selection and improved quality control for this
type of estimation method.
Aerial Surveys ____________________________________________________
Aerial photography has been considered as a potential method of counting
wilderness visitors since the 1960’s. At that time, remote sensing techniques
to measure outdoor recreation use were not feasible, as desired resolution
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would have required flights at altitudes of 500 feet or less (Schnell and Taft
1972). Even with modern improvements in instrumentation and technology,
an estimated maximum of 1,000-foot altitude flights (or a scale of 1:2,000) are
required to obtain the desired amount of image resolution (Aldritch 1979).
Low-altitude flights are incompatible with wilderness values. Satellite
imagery (obtained at a scale of 1:120,000) may be appropriate for monitoring
recreation areas. There are few data which test the relative discrimination
of aerial photographs at different scales and varying degrees of cover. Aerial
photography has been demonstrated to be a reasonable method of measuring
use on some rivers (Becker and others 1980).
Visitor Use Characteristics.—Visitor counts, spatial use patterns, activity
type.
Visitor Burden.—High. Visitors are not contacted directly, but low-altitude
flights are extremely intrusive, and incompatible with wilderness values.
Management Costs.—High. Costs include survey aircraft flight time, pilot
and personnel wages, camera equipment, film purchase and developing, film
viewing and data analysis.
Accuracy.—Undetermined for most wilderness situations.
Comments.—Aerial surveys are probably inappropriate for most wilderness situations, but may be a reasonable method of measuring use on some
rivers (Becker and others 1980).
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Chapter 3: Sampling Methods
Sampling is the systematic strategy by which data are to be collected.
Sampling is essential in some form for all use estimation systems because
proper sampling techniques ensure that the data are representative of the
larger population from which they are drawn. Representative sampling
assures the investigator that the resulting statistics calculated from those
data are reliable estimates of the population values.
There are two general categories of sampling procedures. The first is
convenience or judgment sampling; the data are selected according to the
discretion and subjective knowledge of the investigator. Drawbacks to this
method are discussed in detail below. Probability or statistical sampling
techniques are preferable to convenience sampling because they are based on
the statistical principle of randomization.
We discuss a number of statistical sampling designs appropriate for use in
monitoring wilderness users and use characteristics. Guidelines for selecting the size of the sample are also detailed. General references for sampling
methods and sample size determination include Ackoff (1953), Cochran
(1967), Deming (1960), Scheaffer and others (1986), and Steel and Torrie
(1980).
Convenience or Judgment Sampling _________________________________
Methods based on “professional judgment,” “best guesses,” or “common
sense” are the most frequently used so-called “sampling” techniques. A
recent survey of wilderness managers (covering 423 out of a total of 440
wilderness areas) reported that 63 percent relied on “best guesses” to
estimate visitor use; 61 percent relied on “professional judgment” to formulate regulations (McClaran and Cole 1993). In some cases, on the basis of
previous knowledge and experience, the investigator may consider that
certain well-defined groups are somehow “representative” of the population
as a whole. In other cases, time and logistics may seem to prevent or preclude
the use of statistical sampling methods.
In reality, convenience or judgment samples are an extremely poor
alternative to statistical sampling procedures. The use of human judgment
invariably results in biased sample selection; judgment is unavoidably
influenced by untested assumptions of how the various properties of the
users or visit characteristics, or both, should be related. Furthermore, it is
impossible to determine the size of the bias from sampling methods of this
kind. The samples obtained from judgment surveys are therefore not representative of the population as a whole. Examples are wilderness users that are
convenient or easy to survey, vocal supporters or critics of special interest
groups at public meetings, users surveyed at easily accessed trailheads. The
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characteristics of the individuals sampled will invariably differ from those of
users who travel into more remote or less-accessible areas, or who do not
belong to a special-interest group. Because standard errors cannot be calculated for such samples, statistical testing procedures and analyses cannot be
used.
Statistical Sampling Designs ________________________________________
Why Use Statistical Sampling?
Although the research ideal would seem to entail the complete census of all
possible members of a population, in fact statistical sampling actually results
in substantial accuracy for far less time and cost. Reasons are as follows:
1. Elimination of bias in data collection. Bias inevitably results from
reliance upon personal judgment and wishful thinking, and will result in a
sample that is distorted or otherwise unrepresentative of the population
under study. Appropriate sampling is based on randomization techniques,
which ensure protection against unknown bias.
2. Probability theory can be used to measure the precision of sample
results. Because it is impossible to know the “real” population values, sample
statistics should be selected that estimate underlying population parameters and quantify the certainty of such estimates.
3. Speed. In general, patterns of wilderness visitation do not allow 100
percent monitoring. A complete census might require an entire season or
even years to complete; certain significant segments of the population may
be completely unavailable for censusing. Regardless, extremely large surveys require substantially longer time periods for data processing; additional
costs will be incurred by overtime needed to process extra information and
finding and eliminating mistakes. Much of the same information could be
obtained through sampling in just a few days or weeks.
4. Fewer personnel are required to do the work. Smaller numbers of
personnel make for better and more streamlined selection, training, and
crew coordination. Furthermore, even if sufficient money and resources
could be allocated for the transportation, supplies, and labor required by a
large project, government offices are often constrained by personnel ceilings
that restrict the number of people that can be assigned to a single project.
5. Accuracy and quality of data. Sample information will be more accurate,
first, because crews can be more carefully selected and trained, and second,
because personnel are required to spend relatively less time on the job, thus
reducing fatigue and boredom.
6. Flexibility. Increased speed of sampling means that a canvass can be
conducted and completed at any time; thus, the logistics of the canvass can
be modified relatively quickly to fit the convenience of the study.
7. Reduced visitor burden. Minimizing visitor burden must be a primary
consideration in any visitor use study. Good sampling designs reduce visitor
burden by maximizing the information content for the fewest number of
visitor contacts.
What is a Good Sampling Design?
Because populations are characterized by variability, a good sample design
is characterized as efficient if the sampling variation is as small as possible.
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The standard error of the mean is a measure of the precision of the sample
estimate (that is, how far an average sample mean deviates from the
population mean). Thus, a given sampling design is more efficient than
another if it results in
(1) a smaller standard error with the same sample size;
(2) the same standard error with a smaller sample size.
Simple random sampling is free of bias because every member of the
population has the same chance of occurring in the sample. However, simple
random sampling does not make use of additional information about the
population structure; for example, that hikers are more likely to have a
college education than other wilderness users, or that wilderness users from
one part of the country are more likely to travel further distances to a
wilderness area than those from other parts of the country. The statistical
efficiency of a simple random sampling design can be increased only by
increasing the sample size. Therefore, in many circumstances it may be more
efficient (as well as less costly and time intensive) to use more complex
sampling designs that utilize additional information about the sample.
Sample Size Determination _________________________________________
When planning a wilderness use study, the essential steps to be performed
before the sampling design is specified are definition of the sampling unit,
and determination of the appropriate sample size.
Defining the Sampling Unit
The first step in sample design is definition of the sampling unit. The
collection of sampling units makes up a subset of the population which is to
be sampled; it follows that there must be a clear and explicit definition of the
population of interest in the statement of objectives. The population is all
people, groups, conditions, levels, and so forth, that the investigator wishes
to learn about, whether or not these are available; examples are all wilderness users who buy a certain product, all wilderness users entering a given
wilderness area, all university students, or all commercial outfitters using a
specific wilderness area.
The population is physically defined by the “list” or “frame.” As defined by
Deming (1960), the frame is a set of physical materials that enumerates the
population and allows it to be sampled. The frame must show a definite
location, address, boundary, or set of rules to define the sampling units to be
drawn by the random sampling process. Examples of suitable frames are
maps, directories, membership lists of hunting or outdoors associations,
telephone directories, lists of state license plates, voter lists, permit numbers, and census statistics. Alternatively, there may be no concrete sampling
frame; in these cases a frame may consist of clearly defined rules for creating
and defining the sampling unit. In still other cases it may be impossible to
obtain a representative sample.
Even with a well-designed selection procedure, a poor response rate to a set
of interviews or questionnaire items may invalidate the results of the study.
Suggestions for improving response rates when these techniques are used
are given in part II. However, the problem of nonresponse should be
anticipated in the early design stage and contingency plans made for
handling nonrespondents.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
45
Example: The manager of a wilderness area wishes to determine the
extent of wilderness use during various times of the season. There are several
possible scenarios that dictate the sampling frame chosen:
1. The wilderness area has a strictly enforced permit system; very few
wilderness users enter undetected. Suppose permits numbered 3782 through
10532 were issued for a given year. The manager wishes to mail a detailed
questionnaire to 50 randomly selected wilderness users. The frame, or
listing, of the population to be sampled is the total number of issued permits,
or permit numbers 3782 through 10532.
2. The wilderness area is “open”; that is, there is virtually no regulation of
visitor entry and exit. A potential frame for a given wilderness area is the list
of all households within a 100-mile radius. All households within this area
are numbered, and all those households randomly selected by the sampling
process are enumerated. Some of the sampling units within the sample will
be blank; that is, there are no wilderness users in a given household. Blanks
will be a problem if wilderness users (the feature of interest) are relatively
rare in the population. Considerable time and money may be required to
canvass the sample, only to find few or no representatives of the group of
interest.
3. The wilderness area is “open”, and there is no practical list of potential
wilderness users that could be used to draw up a sampling frame. Instead,
the manager opts for a set of rules defining the frame. The manager defines
a temporal frame consisting of all the days in the entire season; a random
selection of days will provide a random collection of wilderness visitors.
Sample Size
The most frequently asked question when designing a wilderness use study
is “How large a sample?” Unfortunately, there are no simple answers. In fact,
without an estimate of the variability of the response or outcome of interest,
no answer at all can be given. Estimates of the variability must be obtained
from preliminary data obtained either from a pilot study or from data
obtained during previous years.
Most often managers want estimates of the total number of users or an
average of some characteristic of wilderness visitors. These are but two
examples of parameters of interest that will be determined for some sample
of wilderness visitors. If the sampling is in accordance with some statistical
design, then a measure of uncertainty called the estimated standard error for
the estimate will also be developed. This standard error, denoted SE, may be
thought of as the average amount the estimate from (conceptually) repeated
samples will deviate from the underlying population value. Estimates with
small standard errors are more precise than estimates with large standard
errors.
Armed with an estimate of the standard error, a confidence interval may
be constructed using rules of probability. In general, twice the SE added and
subtracted to the estimate form lower and upper confidence bounds that
bracket the unknown population parameter with probability of about 95
percent. This means that there is about one chance in 20 (5 percent) that the
unknown population parameter lies outside such an interval or that the
interval is incorrect. But we are pretty certain, 95 percent (or 19 times in 20),
that the unknown population parameter lies within the confidence interval.
46
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
If a higher level of confidence than 95 percent is desired, the “2” is replaced
by 2.57 for 99 percent. For lower confidence, say 90 percent, the 2 is replaced
by 1.645. Therefore, for a 99 percent confidence interval, 2.57 times the SE
is added and subtracted to the estimate; for a 90 percent confidence interval,
1.645 times SE is added and subtracted.
Formulas in the appendix show how the SE and desired width of the
confidence interval may be used to determine the required sample size for
generating a confidence interval of desired width for a specified level of
confidence for several parameters. Briefly, this is accomplished by setting
the value to be added and subtracted equal to a value and solving for the
sample size, which is an integral part of the SE formula. Further details are
given or referenced in the appendix.
Sampling Designs _________________________________________________
Simple Random Sampling
Simple random sampling, or random sampling without replacement, is the
selection of items from the population such that each item has an equal
probability of being selected. That is, the selection of the sample is entirely
due to chance; it does not mean that selection of a sample is haphazard,
unplanned, or based on guesswork.
The random selection of items is performed by means of a random number
table. A random number table is a sequence of numbers generated by
(conceptually) repeatedly drawing numbers from 0 through 9 from a hat,
replacing each number before the next draw, such that each digit 0 through
9 has an equal probability of occurring in each position in the sequence.
Therefore, we have no reason to expect that any one number will appear more
often than any other number, nor that any sequence of numbers should occur
more often than another sequence, except by chance. Table 3 contains 2,000
computer-generated random digits arranged for convenience in 10 columns
and 40 rows of 5-digit groups.
How to Obtain a Random Sample
Suppose we want a random sample of size n from a population of size N. We
will draw n consecutive numbers from the random number table in table 3,
ignoring any number greater than N, and any number drawn for the second
time (if we are sampling without replacement). If the population is less than
100, we are required to draw a sample of n two-digit numbers; if n is equal
to or larger than 100 and less than or equal to 999, we will be required to draw
a sample of n consecutive three-digit numbers, and so on. The start point may
be anywhere in the table, but a more satisfactory method is to poke at any
spot in the table with a pencil, read the four digits closest to the pencil point,
and use those to locate a start point. Digits read in any direction are
random—left to right, top to bottom, and so forth.
Procedure for Random Sampling
1. Obtain a list or “frame” for a population of size N; number each item in
the frame.
2. Decide on the appropriate sample size n to be drawn from the population.
3. Pick n random numbers from the random number table, excluding those
that are greater than N. If the end of the table is reached, simply “wrap” up
to the top.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
47
Table 3—Random number table.
Row
Column
5
6
1
2
3
4
7
8
9
10
1
2
3
4
5
10486
73679
63865
49726
54523
24171
78358
21629
40330
34394
46732
79152
21229
44578
91794
28740
99760
09131
39100
42527
26899
84501
27787
14112
31970
19318
58832
15262
30815
94092
44151
44612
65766
21024
08841
05478
98740
44905
47700
01786
65089
19052
28331
20198
04623
13978
36084
07628
32921
70491
6
7
8
9
10
01822
97111
26649
29713
75572
33331
41959
22013
91004
94458
94062
87141
57096
21915
30359
18259
28730
15949
47233
96818
15477
19725
38399
19757
12370
99842
63425
96190
23067
98566
49073
42713
86375
47654
82734
61869
79053
60585
84324
74119
57548
89896
84033
53456
57274
36566
88309
92924
64015
21327
11
12
13
14
15
51353
42146
59492
49613
87528
82896
99692
61189
85175
99124
34206
65221
23032
55232
85858
44715
48951
22544
21373
24274
46721
34071
38697
54868
94713
52506
71623
98425
03444
62191
52375
67643
71524
37782
43189
17401
81184
57779
46427
52137
75584
27069
84992
22917
96329
05222
52048
11737
63802
63053
16
17
18
19
20
21
22
23
24
25
38404
42298
53635
41576
32611
51569
92326
24430
16956
35743
34306
87135
03919
20335
61789
86030
24128
51212
93082
50061
23636
56083
10864
40541
62034
57005
14447
71687
85099
36735
61542
23148
52861
09596
52161
78733
27220
17866
94246
93985
68318
12226
97661
24638
83326
38783
70432
72434
96284
91804
43052
87360
37910
47172
71415
32056
00403
37132
92649
49702
44517
66392
81404
38594
71683
93193
55787
37025
78831
87864
57935
01842
64731
50446
14277
71194
89970
54517
48646
95530
41493
47682
34166
38071
94489
64960
45706
61746
28247
35266
21232
05849
12428
41489
86411
13532
90644
95219
08542
76978
26
27
28
29
30
45371
22031
58625
18256
67460
94239
71445
14121
46418
37690
58168
27735
72519
81212
09210
55388
41272
36231
48594
23301
77872
49040
99379
19727
99668
64363
36759
17692
32483
78223
78120
11921
70647
61344
40589
58078
81538
34479
79533
79996
87229
03294
59956
32039
63419
96888
53928
23509
13373
04596
31
32
33
34
35
95316
99806
97548
88279
80223
35722
85844
17286
52919
73728
32124
78984
51371
09766
83290
47004
01557
97245
91898
77247
40391
59797
45991
90506
07426
25743
32480
47590
65424
58769
11719
26817
99571
10383
59858
23695
20216
02891
41660
48176
73648
81800
03712
53965
58750
22306
42301
14906
62208
80039
36
37
38
39
40
57685
47053
12516
87686
24452
44187
79853
13362
90153
00090
34178
83152
77021
54670
42790
88661
69627
97117
49189
70979
19728
69031
80076
86081
96357
97953
37207
24403
65526
50047
02030
63480
29688
54774
25974
29292
20292
04008
97169
60145
60970
73725
13554
19535
39649
50840
48762
93159
81816
10062
4. Obtain the observations for the items whose identification number
corresponds to the selected random numbers.
Example: Suppose we need to select a sample of size n = 10 from a
population of size N = 30.
1. In the random number table (table 3), the pencil falls on the digits 32039
in row 29 and column 9.
48
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
2. Go to row 32, column 3 (ignore the last digit) as the start point.
3. Record 10 consecutive pairs of digits less than or equal to 30 by moving
right from the start point. The first eight “usable” numbers are 15, 24, 26, 02,
16, 04, 23, 01. At this point, the line ends; proceed by dropping down to the
next line. The remaining two numbers are 19 and 14.
Advantages of Random Sampling
1. It is fair—every item in the population has an equal chance of being
selected and measured.
2. It protects against bias or misrepresentation of the population.
3. It allows easy data analysis and error calculation.
4. It requires minimal prior knowledge of the population; that is, no
further information is required as to how the population is structured.
Disadvantages of Random Sampling
1. It is less statistically efficient than other sampling methods.
2. It does not make use of additional knowledge of how the population is
structured.
3. It may be difficult or extremely expensive to implement because all
potential sample items must be able to be inventoried or listed.
Systematic Sampling
Systematic sampling is an approximation of random sampling. The sample
is obtained by randomly selecting the first item of a sample; the remaining
items are selected by systematic selection of each item at some predetermined interval. Examples of systematic sampling schemes in wilderness use
estimation are the selective censussing of every tenth wilderness user, every
fifth car passing a checkpoint, or every fourth group of visitors encountered
during a day of ranger patrol.
Procedure for Systematic Sampling
1. Given a population of size N, determine the appropriate sample size n.
2. Calculate the sampling interval k between selected items; k is calculated
as the ratio N/n. This ratio is then rounded off to the nearest whole number.
3. Using the random number table, randomly select some number i
between 1 and k.
4. Sample the items identified by the following sequence of numbers:
i, i + k, i + k + k, i + k + k + k, ...., and so forth
or
i, i + k, i + 2k, i + 3k, ...., and so forth
Advantages of Systematic Sampling
1. Systematic sampling may reduce variability (it may be more efficient than
random sampling), especially if there are patterns or time-order in the data.
2. It is simple to perform (because only one random number is required).
3. Sampling effort is guaranteed to be distributed evenly over the population.
Disadvantages of Systematic Sampling
1. There is only a limited number of different possible samples; since every
kth item is sampled after a random start, there are only k distinct samples.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
49
This is in contrast to the almost limitless number of different possible
random samples.
2. Estimates may be severely biased if there are any patterns in the data.
For example, if the sampling units were days over the entire summer season,
and if the 1 in k sampling interval happened to coincide with multiples of 24
hours or 7 days, the same time period would be sampled each day or week.
3. There is no reliable method of estimating the standard error of the
sample mean.
Example: Suppose we wish to select 25 permits from a total of 8,743 permit
applications. The sampling interval is then 8,743/25 = 349.7 or 350. If the
permit cards were arranged in numerical order, we would select a random
number between 001 and 350 as the first element of the sample. Suppose this
random number was 074; the permits for the sample would be found by
successively adding 350 to successive numbers in the series; in other words,
we would select permits numbered 74, 424, 774, ..., 8474.
Frequently, permits are stored haphazardly in drawers or boxes, and are
not in numerical order. In these cases, much time and labor would be
required to either sort or renumber permits to allow randomization. However, we can use an alternative sampling method which utilizes a given
height of the permit stack as a selection criterion rather than an assigned
numerical interval. For example, suppose the 8,743 permits are in a stack or
drawer 75 inches in depth. Choose a random number i from the range 001 to
350. Count to the ith permit from the front of the stack. From that permit,
select 25 permits at 3-inch intervals.
Computations for Systematic Samples
If the analyst is confident that the systematic sampling produced a sample
free of bias due to patterns in the ordering of data, the sample can be
considered equivalent to a simple random sample for analysis.
Multiple Systematic Sampling
Samples obtained from a systematic sampling procedure may be severely
biased if there is any form of cyclic variation in the data and the interval
between consecutive sampling units equals the period of the variation. Some
protection against this form of bias can be obtained by partitioning the
sample into m groups, and changing the random start number for each group.
If the desired sample size is n, then each group will be of size ng = n/m. For
example, suppose the total sample size desired is 30. Therefore, a possible
sampling scheme would involve selecting a sample divided into m = 5 groups,
of size ng = 30/5 = 6 each. A new random start number is then selected for each
of the m groups.
Computations for Multiple Systematic Samples
Example: For the East Hickory Creek trail data (table 4), we wish to
estimate the mean number of users over the summer season. We have a
sequence of 112 consecutive days, and require a sample of size n = 20. The
sampling interval is thus 112/20 = 5.6; that is, we are required to sample one
day in every 5. To select the random starting position, choose a number
between 1 and 5 from the random number table. Record this number, add 5
to obtain the second number, and so on. For example, suppose the random
50
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Table 4—Estimated daily user and group counts for East Hickory Creek Trail during a 16-week summer season in the Cohutta
Wilderness.
Time
Wk
Day
Usr
Gp
Time
Day
Wk
Usr
Gp
Time
Wk
Day
Usr
Gp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
1
1
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
3
3
3
4
4
4
4
4
4
4
5
5
5
5
5
5
5
6
6
6
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
57
46
11
19
21
13
13
58
57
10
13
11
4
10
34
65
13
5
15
31
21
41
41
36
11
5
13
12
43
43
12
6
8
12
5
45
47
9
26
23
7
8
11
6
9
31
27
5
7
6
4
6
17
26
6
4
10
9
6
25
21
7
5
5
6
3
24
24
6
5
4
7
5
25
23
7
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
6
6
6
6
7
7
7
7
7
7
7
8
8
8
8
8
8
8
9
9
9
9
9
9
9
10
10
10
10
10
10
10
11
11
11
11
11
11
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
28
14
9
9
33
57
10
8
9
19
13
69
58
18
13
7
5
5
41
57
7
15
14
10
7
83
47
8
8
9
12
15
27
43
15
7
17
11
5
9
5
5
16
29
5
3
9
10
7
28
24
8
6
5
2
2
25
28
6
6
9
4
6
34
26
5
5
6
6
7
17
22
7
4
7
8
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
11
12
12
12
12
12
12
12
13
13
13
13
13
13
13
14
14
14
14
14
14
14
15
15
15
15
15
15
15
16
16
16
16
16
16
16
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
13
75
33
21
34
7
9
8
28
38
14
9
20
18
14
27
48
3
26
8
11
10
78
34
7
18
12
16
11
26
53
16
16
9
25
14
7
30
19
9
9
5
4
7
19
21
9
3
7
7
7
17
24
1
7
5
6
8
29
19
4
5
7
5
4
16
24
4
6
5
8
5
start number chosen is 2. The days to be sampled are then 2, 2 + 5 = 7, 7 + 5
= 12, 12 + 5 = 17, and so on. The resulting systematic sample is as follows:
Day
No.
users
2
7
12
17
22
46
13
11
13
41
No.
Day users
27
32
37
42
47
13
6
47
9
9
Day
52
57
62
67
72
No.
users
18
41
10
8
43
No.
Day users
77
82
87
92
97
13
7
14
27
11
The sample mean for the number of users is 20.0, and the estimated standard
error, or SE, is 2.98.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
51
However, a time plot of the data shows that the number of users increases
dramatically on weekends (fig. 4); the data are in fact strongly periodic. As
a result, the estimates for the mean and standard error will be biased. We can
correct this bias to a certain extent by frequently changing the random start
number; in other words, by performing multiple systematic sampling.
We decide to draw m = 4 systematic samples, each of size n = 5. The
sampling interval k is 112/5 = 22.4, or 22. Thus, we need to choose 4 random
numbers between 1 and 22. In this example, the random numbers are 17, 6,
12, and 13. The 4 samples are as follows:
Sample 1
No.
Day users
17
39
61
83
105
Means
Sample 2
No.
Day users
13
28
14
9
11
15.0
6
28
50
72
94
13
12
69
43
3
28.0
Sample 3
No.
Day users
Sample 4
No.
Day users
12
34
56
78
100
13
35
57
79
101
11
12
5
75
34
27.4
4
5
41
33
7
18.0
The mean of the 4 sample means is 22.1. For a sub-sampling approach such
as this, the standard error is estimated directly from the four sample means,
that is:
SE = [(15.0 − 22.1)2 + (28.0 − 22.1)2 + (27.4 − 22.1)2 + (18.0 − 22.1)2 ] /(4 − 1) / 4 = 3.292
Stratified Sampling
Stratified sampling assumes that an extremely diverse, or heterogeneous
population can be divided into non-overlapping groups; these groups are
referred to as strata. A random sample of items is selected from each stratum.
Number of Users
100
80
60
40
20
0
0
14
28
42
56
70
84
98
112
Time (days)
Figure 4—Time plot of the number of visitors using the East Hickory Creek
trail in the Cohutta Wilderness during a single summer season.
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These samples are then combined to form a single estimate for the population
under consideration. Strata may be very different from one another, but
should be homogeneous within each strata. Examples of strata are types of
users (hikers, horse users, hunters, mountain bikers), amount of trail use
(“light,” “moderate,” “heavy”), gender (male, female), user education levels,
and trailhead elevation (high, low).
Procedure for Stratified Sampling
1. Identify the sampling unit.
2. Decide on the total sample size N (number of visitors to be surveyed).
3. Define the strata.
4. Determine sample size ni for each stratum (see below).
5. Draw random sample of ni items from each stratum.
6. Take complete data for each randomly selected item from each stratum.
Choosing Stratum Sample Size
There are three procedures for selecting the appropriate sample size for
each stratum: proportional, disproportional, and optimal allocation.
1. A proportional sample is chosen so that the number of items selected
from each stratum is proportional to the size of the strata. That is, a fixed
percentage of each strata is sampled.
2. A disproportional sample results when the number of items selected
from each stratum is independent of its size. A disproportional sample
naturally results when the sample size for each stratum is constant.
3. Optimal allocation results in a sample size proportional to both the size
of the sampling units and the variance within each stratum; estimated costs
associated with each sample may also be incorporated into sample size
computations. To estimate sample size with this method, preliminary estimates for both costs and strata standard deviations must be obtained from a
pilot study, or from surveys performed in previous years. Estimates can be
easily obtained if the population can be sampled repeatedly; estimates need
not be highly accurate to give satisfactory results. If the standard deviation
and the cost of sampling are the same for all strata, this method is the same
as proportional allocation.
Advantages of Stratified Sampling
1. If each stratum is relatively homogeneous and there are large differences between strata, stratified sampling is more statistically efficient than
simple random sampling.
2. Sample sizes can be chosen separately for each stratum. This is important when different elements of the population must be handled separately
or they present different problems of listing and sampling. The investigator
has more freedom in allocating resources to sampling within each stratum.
Disadvantages of Stratified Sampling
1. Strata must be well defined so that items may not inadvertently be
classified into more than one group.
2. There must be accurate information available on the proportion of the
population in each stratum.
3. There may be considerable costs associated with the preparation of
stratified lists.
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53
Example: There are 50 trailheads (the sampling units) classified by
relative amount of use, defined here as the number of visits per day at a given
trailhead. Four strata of use can be defined: “light use” (≤2 visits/day),
“moderate use” (3-9), “medium use” (10-19), and “heavy use” (≥20). The
manager has resources sufficient to monitor only 17 trailheads.
In this example, Ni represents the number of trailheads in each use
category (i = 4), ni is the number of sample trailheads to be selected from each
use category, and fi = ni/Ni is the sampling fraction for each use category.
Then, the sampling effort required for a proportional and disproportional
stratified random sample is as follows:
Stratum:
number of
visitors
per day
Ni
2 or less
3 to 9
10 to 19
≥20
24
15
8
3
8
5
3
1
Total
50
17
Proportional
ni
fi
0.33
0.33
0.33
0.33
Disproportional
ni
5
5
4
3
fi
0.21
0.33
0.50
1.00
17
The manager decides to concentrate sampling effort on the more heavily
used trailheads, while minimizing sampling effort on the less frequently
used trailheads. This decision is justified on several grounds. First, more
heavily used trails are expected to have a larger influence on the overall
estimate of wilderness usage. Second, because potential impact is correlated
with use, monitoring the heavily used trails will provide a more reliable
means of gauging environmental damage. Thus, the manager opts for the
disproportional sampling scheme.
Computations for Stratified Samples
Since stratified sampling selects a simple random sample from each strata, the
initial analysis requires calculation of a sample mean and estimated standard
error of the sample mean for each strata. Strata sizes are then used as weights
in computing weighted averages of the strata means and standard errors.
Cluster Sampling
Many types of populations in wilderness studies are difficult or impossible
to enumerate completely. For example, it is impossible to draw up a list of all
potential wilderness users. However, it may be possible to identify certain
subgroups, or clusters, relatively easily. Cluster sampling involves a simple
random sample of clusters, with the complete census of all items in each
cluster. Clusters are similar, or homogeneous, units, with a high degree of
diversity, or heterogeneity, within each cluster. These characteristics of
cluster sampling contrast to those found in a stratified sample where a
random sample is selected within each stratum, and strata are themselves
diverse with a high degree of within-stratum homogeneity.
Typical clusters are geographical units or areas, social units (such as
households, families), agencies, or temporal units. For example, suppose we
require an evaluation of impact in nondesignated campsite areas in a given
wilderness area. It would take far too much time, resources, and personnel
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to systematically search the entire area. Instead, we might define quartersections as the clusters. Then we would randomly sample clusters in a given
wilderness area, locate and enumerate all campsites occurring in the sampled
clusters. Stopping all cars for interviews with occupants on randomly
selected days would be one example of a temporal cluster, expected maximum
heterogeneity within the day and homogeneity across days.
Procedure for Cluster Sampling
1. Define the “cluster” to be used as sampling unit.
2. Number clusters sequentially from 1 to N.
3. Determine the appropriate number of clusters to be sampled.
4. Draw a random sample of clusters.
5. Take complete data from each of the sampled clusters.
The efficiency of cluster sampling may be increased further by stratification, reducing cluster size, and subsampling. See Ackoff (1953) for details.
Advantages of Cluster Sampling
1. Relatively low field costs, since it requires the enumeration of individuals in selected clusters only.
2. The characteristics of clusters, as well as those of the population, can be
estimated.
3. Data can be combined with those obtained in subsequent samples, since
clusters, not individuals, are selected.
Disadvantages of Cluster Sampling
1. It has lower statistical efficiency than other sampling techniques.
2. Each member of the population must be uniquely assigned to a cluster;
this may be difficult if the characteristics defining the cluster are ambiguous.
3. Cluster properties may change so that the cluster sample may not be
usable in later data analysis.
Effects of Sample Design on Use Estimates: A Case Study
As part of a study estimating visitor impact in the East Hickory Trail in the
Cohutta Wilderness, visitor counts were obtained on a daily basis over the
entire summer season (table 4 and fig. 4). The manager’s immediate objective
was to estimate the daily average number of users. To illustrate the effects
of sampling method on the efficiency of the sample estimate, we analyzed the
same data set using several sampling techniques.
The sampling frame is the total number of days in the season, or N = 112
consecutive days, from the beginning to the end of the summer season.
Assume that a sample size n = 20 will allow estimates of the preferred
population characteristics with the required precision.
1. Random sampling. We need to select 20 consecutive three-digit
numbers between 1 and 112. Suppose the randomly selected start point
occurred on row 36, column 7. Thus, the first random triplet is 020, or 20. The
next three-digit number, 302, is larger than 112, and is discarded, as are the
next 13 sets of triplets. The next two “usable” random numbers are 031 and
076. The triplet 020 in row 37 columns 7 and 8 is less than 112, but was
selected previously; this second value is discarded. In this example, the
unique set of random numbers obtained was as follows: 020, 031, 076, 040,
081, 015, 090, 097, 006, 054, 084, 052, 107, 033, 044, 001, 101, 046, 049, 073.
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Once the entire set of 20 random numbers is obtained, the numbers are
ordered and observations are made on those days. The data are:
Day
No.
users
No.
Day users
1
57
33
6
15
20
31
13
34
31
12
40
44
46
49
Day
No.
users
No.
Day users
8
52
18
84
8
14
57
8
13
54
73
76
81
7
15
11
34
90
97
101
107
18
11
7
53
The estimated mean number of users is 21.45 (the mathematical average)
and the standard error is 3.79 (from computations described in the appendix).
2. Systematic sampling. Computations for systematic sampling follow
those for simple random samples. The standard error is 3.44.
3. Multiple systematic sampling. Computations for multiple systematic sampling are given in Chapter 3: Sampling Methods. The standard error
is 3.292.
4. Stratified sampling: proportional n. The manager decided to stratify
days on the basis of relative use, as defined by the number of visitors entering
the area. “Light” use occurred on normal business days (Monday through
Friday), whereas weekends (Saturday and Sunday) were characterized by
“heavy” use. There are therefore two strata, weekdays and weekends. In a
112-day season, there were 80 weekdays and 32 weekend days.
For a proportional stratified sampling design, the manager could afford to
take 20 observations, which is about 18 percent of the 112 day season or 18
percent of 32 and 80, which gives 6 and 14 days allocated between the
weekend days and the week days. For convenience, a systematic sample was
used in each stratum after the days in each stratum are numbered separately. The first stratum (“weekday”) consists of 80 days; therefore the
sampling interval is 80/14 = 5.7, or 6, and the start value is selected from the
random numbers between 1 and 6. There are 32 days in the second (“weekend”) stratum. Therefore the sampling interval will be 32/6 = 5.3, rounded to
5, and the start value will be chosen by selecting a random number between
1 and 5.
Suppose the random start values for each stratum are 4 and 1 respectively.
Then the two stratified samples are as follows:
Weekend days
Day No. users
4
9
14
19
24
29
Mean
SD
57
43
57
83
33
78
58.5
19.37
Weekdays
Day No. users
Day No. users
1
7
13
19
25
31
37
11
13
15
13
5
10
13
43
49
55
61
67
73
79
14
12
13
14
26
12
25
14.0
5.43
The combined estimate of the population mean is: (32/112)·(58.5) + (80/
112)·(14.0) = 26.71 with an estimated standard error of 2.25.
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5. Stratified sampling: disproportional n. For a disproportional sample,
the sample sizes for each group will be the same; that is, n1 = n2 = 10. The
sampling interval for the weekend stratum is 32/10 = 3.2, or 3, and the start
value is a random number between 1 and 3. For the weekday stratum, k is
80/10 = 8, and the start value is a random number between 1 and 8. Suppose
the random start values were 1 and 4 for the first and second strata
respectively. Then the sample days and their corresponding data are as
follows:
Weekend days
Day
No. users
1
4
7
10
13
16
19
22
25
29
Mean
SD
57
57
41
43
33
58
83
43
28
48
Weekdays
Day
No. users
4
12
20
28
36
44
52
60
68
76
49.1
15.63
13
5
12
14
18
10
7
8
8
16
11.1
4.20
The combined estimate of the population mean is 21.96 with an estimated
standard error of 1.62.
The results for the five types of sampling procedures are summarized as
follows:
Sampling method
Estimated population mean
Standard error
Random
Systematic
Multiple systematic
Stratified:
proportional
Stratified:
disproportional
21.45
20.00
22.10
3.44
2.98
3.29
26.71
2.25
21.96
1.62
Note that the estimated population means differ for each of the five
sampling methods since they use different samples, but all are reasonably
consistent. Random sampling is least efficient because it has the largest
standard error in comparison with other methods with the same sample size.
Stratified sampling gives the most efficient sample estimates.
Field Sampling Strategies
Sampling strategies must be developed for scheduling the rotation of
“observers” across trailheads, scheduling “observer” effort (observation periods), calibration, compliance estimation, and visitor selection.
Scheduling “Observer” Rotation Across Trailheads
Monitoring every access point is feasible only if the wilderness area has
relatively few access points and funding is not restricted; in this case, a
rotation strategy is not required. However, it is more likely that the number
of available “observers”—mechanical counters, human observers, cameras,
or registration stations—will be insufficient for large-scale monitoring.
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57
Therefore, available resources must be rotated systematically. Rotation
schedules will depend on the number of access points to be surveyed and the
frequency for which use estimates are required.
Rotation strategies are determined primarily by perceived differences in
use occurring in either space or time. We recommend a more-or-less permanent allocation of an “observer” to each high-use trailhead; the overall
accuracy of total use estimates will depend primarily on the accuracy of
estimates obtained for high-use trailheads.
As a general rule of thumb, it is suggested that an “observer” is allocated
to the trailhead with the highest amount of visitor traffic; other “observers”
are rotated systematically across the remaining trailheads, such that the
amount of time allocated to each trailhead is proportional to the use that
trailhead is expected to receive.
Scenario 1. Suppose a manager must monitor use at four trailheads, but
only two mechanical counters are available. One trailhead is believed to
account for about 60 percent of use in that wilderness area; a second trailhead
is believed to account for about 20 percent of the use and the two remaining
trailheads receive an equal amount of the remaining use. Therefore, the
second counter is allocated to the second trailhead for half of the time, and
allocated between the two remaining trailheads in proportion to anticipated use.
Scenario 2. Suppose use estimates are required for an entire wilderness
area over an entire season. It has been determined by preliminary surveys
that use patterns are fairly stable within a particular geographic section of
the wilderness area, but extremely variable over the use season. Therefore,
widespread sampling of the wilderness area is required.
Strategy: Account for use in each section by allocating one counter
for every x access points.
Scenario 3. Suppose more intense sampling of a particular section is
required, but use patterns are sufficiently stable such that monitoring every
other year is sufficient to generate adequate use estimates.
Strategy: (1) Divide wilderness access points into two to four sections, such that each section contains an equal number of access
points or trailheads (say four or five); (2) place counters on all
trailheads within a randomly selected section for 1 year; (3) rotate
counters to a new section each year.
This strategy would reduce costs associated with moving counters;
the obvious disadvantage is that use estimates for a given section can
be obtained only every 2 to 4 years.
Example. Suppose the manager wishes to estimate use for the entire 16week summer season; there are four trailheads and two mechanical counters.
One counter is permanently allocated to the high-use trailhead, leaving
three trailheads to be monitored with one counter. The 16-week season is
partitioned into eight 2-week blocks. The counter will be allocated to each
trailhead for two separate time blocks; this leaves two blocks as discretionary
time.
The order in which the counter is assigned to each of the three trailheads
is determined randomly. Suppose the random number sequence for the eight
time blocks is 5 7 8 3 2 6 1 4, and the random sequence for the three trailheads
is 3 4 2. Then the counter will be assigned to trailhead 3 on time blocks 5 and
7, to trailhead 4 on time blocks 8 and 3, and to trailhead 2 for time blocks 2
and 6.
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Scheduling Observer Effort
Observation periods are determined by partitioning the visitor season into
defined time blocks, numbering the blocks, then randomly selecting the time
blocks for which observations are to be made. The length of the observation
period is determined by operational convenience; it may be measured in
minutes, hours, days, or weeks. As a general rule of thumb, “observers”
should be placed at each trailhead for at least two observation periods.
Example. A preliminary study of use patterns in a certain wilderness area
suggests that the number of visitors is fairly constant over the season. It was
observed that approximately 20 percent of wilderness users entered the area
on weekdays, another 40 percent of users entered on Saturday mornings, 10
percent on Saturday afternoons, 20 percent on Sunday mornings, and 10
percent on Sunday afternoons. A total of 10 observation periods can be
sampled with the resources available.
The manager decided to partition the sampling day into morning and
afternoon time blocks. Time blocks were further stratified into three operationally defined use categories: low, medium, and high. Observer effort was
allocated in proportion to amount of use. Thus 20 percent of sampling effort
was allocated to low-use periods (that is, two time blocks occurring on either
a weekday morning or afternoon); 40 percent effort to high-use periods (four
Saturday mornings), and the remaining effort to medium-use time periods
(one Saturday afternoon, two Sunday mornings, and one Sunday afternoon.
The specific time blocks to be monitored were selected by random sampling.
The entire monitoring period required for this sampling plan is approximately 4 weeks.
Calibration
Calibration requires that observations obtained from the primary counting
device (usually a mechanical counter) are paired with observations obtained
by a method of known accuracy (either human observers or cameras). The
number of calibration samples to be taken will depend on the amount of
precision required, the resources available for calibration, and the relative
stability of use over time. The accuracy of calibrations must be spot checked
at intervals and updated as required; if use patterns change substantially
over the season, calibrations made at the beginning of the season will not be
applicable to counts made later in the season.
Camera Calibration.—Use of hidden cameras requires a minimum amount
of personnel involvement. Cameras are installed on the traffic area where the
item to be calibrated (mechanical counter, registration station, and so forth)
is installed. To maximize the efficiency of the method, cameras must be set
up so that traffic will be visible for long distances.
There are two general sampling strategies for camera calibration: fixedinterval monitoring and counter-activated monitoring.
(1) Fixed-interval monitoring. The camera is activated at programmed
time intervals; all traffic during a sample period is photographed. Specific
intervals are selected by random sampling procedures.
(2) Counter-activated monitoring. The camera is attached to a mechanical
counter, and takes photos only when the counter is activated by visitor
traffic. This technique provides a measure of overestimation bias only; it does
not provide information on error occurring because of visitors undetected by
the counter. An alternative may be to have a separate activator for the camera.
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59
For example, a counter may be activited by an active infrared sensor, while
the camera is activated by a passive infrared sensor, or a very sensitive
seismic sensor.
Calibration by Human Observers.—Calibration with observations taken
by human observers is more labor intensive than use of cameras, but is more
accurate. Observers should be stationed close enough to the item to be
calibrated (counter, registration station, and so forth) so that all traffic is
observed; although observers need not be exactly by the check point, they
should not wander up and down the trail.
Scheduling of agency personnel may have to occur within the confines of the
workweek. However, if significant amounts of use occur outside of normal
working hours, it is essential that these time blocks are covered; volunteer
labor may be one option. Observer fatigue and boredom may be a significant
problem if time blocks are extremely long and few visitors are encountered.
Sampling effort may be apportioned according to operationally defined
amounts of relative use observed per time block. At least two observation
periods should be scheduled for each category.
Compliance Estimates
Compliance is the estimate of the number of visitors who actually register
or obtain permits. Compliance estimation is essentially similar to the
calibration procedures described above; visitor registration is “calibrated” by
supplementary observations so that the number of wilderness users who do
not register can be accounted for, and total visitor counts can be adjusted
accordingly. The number of supplementary observations taken will depend
on the amount of precision required, the resources available for compliance
checks, and the relative stability of visitor use over time. If use patterns
change substantially over the season, registration rates or permit compliance rates estimated at the beginning of the season will not be applicable
later in the season; the accuracy of registration rates must be spot checked
at intervals and updated as required.
Frequently, permit or registration compliance estimates are obtained in
the course of routine wilderness ranger patrol. In the so-called “roaming
observation” technique, rangers check for compliance as visitor groups are
encountered, and tally the proportion of those encountered who are not in
compliance. However, this type of visitor sampling results in highly biased
estimates of visitor use. Bias occurs for a number of reasons: (1) because the
probability of visitor contact depends on when and where the observer
travels, (2) scheduling is not random but deliberately selected to coincide
with periods of heaviest use, and (3) the probability that a visitor group will
be encountered is proportional to the length of time spent in a given area,
observer location in relation to visitor distance traveled, and so on.
Unbiased data can be obtained only by implementing predetermined
statistical sampling strategies. Permit checkpoints are established in accordance with a spatial sampling scheme (see above); sampling of visitors at
each checkpoint may be completely random, systematic (for example, selective censusing of every tenth wilderness visitor, or every fifth car passing a
checkpoint), stratified, or a combination of these.
Determining Total Population Size from Compliance Sampling.—The size
of the total wilderness visitor population is estimated by the direct sampling
procedures used to estimate compliance or registration rates. The method is
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analogous to the Peterson or Lincoln capture-recapture indices used in
wildlife population estimation. It should be used whenever total population
size is to be estimated from ratio data.
The total number of visitors in a given time period is N, the quantity to be
estimated. The total number of permits issued (or registration cards completed) is t. At some period during the visitor season, wilderness rangers
survey n visitors, of which s are found to be in compliance (that is, have
actually obtained a permit or registered). Then the compliance rate is
estimated as the proportion of the surveyed sample, or r = s/n. The total
population is estimated as:
n
t
Nˆ = ⋅ t =
s
r
The 95 percent confidence interval is N ± 2 · SE, where SE is approximately
t 2 ⋅ n(n − s)
.
s3
Example. A total of 300 permits were issued for a given wilderness area.
Subsequently, the wilderness ranger randomly sampled 50 visitors, of which
30 had permits. The compliance rate was therefore r = 30/50 = 0.6, or 60
percent. The total number of visitors entering the area was estimated as N
= 300/0.6 = 500, with a 95 percent confidence interval of approximately 500 ±
SE =
2
(300)2 ⋅ 50(50 − 30)
≅ 500 ± 115, or between 385 and 615 visitors.
(30)3
Visitor Selection
The sampling strategy for visitor selection requires both an estimate of the
sample size, and a time schedule. Unless the wilderness area has a strictly
enforced permit program, visitors cannot be randomly selected prior to
arrival. If there is no regulation of visitor entry and exit, the investigator
must make a random selection of “contact days”, followed by random
selection of visitors within the contact day. Sampling may be completely
random, systematic (for example, selective censusing of every tenth wilderness visitor, or every fifth car passing a checkpoint), stratified, or a combination of these.
The number of visitors that must be sampled is determined with reference
to the population of interest, the type of response variables to be measured
(categorical, count, continuous), the expected variation of the response
variables, and the specified sampling strategy. Determination of the appropriate sample size requires a preliminary estimate of the variability in the
observations. Preliminary estimates are obtained from a pilot study, or from
data collected in previous years.
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Part II: Selecting and
Building a Use
Estimation System
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Introduction
There are 10 major use estimation systems described in separate sections
within part II. Each section is divided into two parts consisting of a System
Description and a description of the Operational Procedures. Operational procedures are detailed in a series of steps, with their number varying
according to the particular system of interest. Procedural guidelines are
given for the following elements:
1.
2.
3.
4.
5.
6.
Use characteristics that can be measured with the particular system
Measurement techniques
Equipment purchase
Equipment installation
Data collection strategies
Visitor use calculations
Because each section is intended to be self-contained, there is some overlap
in information between sections. Additional information required for implementing the specifics of data collection, sampling strategies, and data
analysis are discussed in part I.
The 10 use systems are summarized (table 5) in terms of two organizational
categories: information category and data collection techniques. Each
column represents a system, designated by a capital letter (A, B, C, and so
forth), followed by the page number indicating where that system is described. The components of each system are indicated by an X in the
appropriate row representing various required components. The potential
for each system to provide needed information is evaluated through categorization of potential objectives:
I. Visit counts
II. Observable visit and visitor characteristics
III. Simple nonobservable characteristics (easily reported information implying minimal visitor burden—for example, length of stay, age)
IV. Complex nonobservable characteristics (more complicated or involved information, implying increased visitor burden—for example, attitudes, opinions)
V. Summary use statistics
The use of table 6 is illustrated in the following example. Suppose the stated
management objective is to obtain a visit count for a certain time period.
Table 5.I. (“Visit Counts”) shows that all systems A through J provide that
information; thus, choice of a system will be dictated by cost and ease of
implementation. However, suppose information must be obtained on some
nonobservable visit characteristic such as length of stay. Table 5.III. (“Simple
Nonobservable Visit and Visitor Characteristics”) shows that systems A, B,
and D will not provide this information at all; options are restricted to the
remaining seven systems.
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Table 5—Summary of 10 user-estimation systems categorized by information category and system elements.
System A. Mechanical counters with visual calibration
System B: Mechanical counters with observer calibration and sample observations
System C: Mechanical counters with observer calibration and sample interviews
System D: Visitor registration system with checks for registration rate
System E: Visitor registration system with registration rate checks and sample interviews
System F: Permit system with compliance checks
System G: Permit system with compliance checks and sample interviews
System H: Permit system with compliance checks and mailback questionnaires
System I: Indirect counts
System J: General visitor surveys
Table 5 (cont.)
I. Visit Counts
(individual counts, group counts)
Data collection techniques
Mechanical counters
Visual calibration (accuracy)
Sample observations
Sample interviews
Visitor registration
Registration rate check
Sample interviews
Permits
Permit compliance checks
Sample interviews
Sample mailback surveys
Indirect counts
General visitor surveys
A
p. 68
B
p. 79
C
p. 90
X
X
.
.
.
.
.
.
.
.
.
.
.
X
X
X
.
.
.
.
.
.
.
.
.
.
X
X
.
X
.
.
.
.
.
.
.
.
.
Use estimation system
D
E
F
G
p. 101 p. 110 p. 121 p. 128
.
.
.
.
X
X
.
.
.
.
.
.
.
.
.
.
.
X
X
X
.
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.
.
.
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.
.
.
.
.
X
X
.
.
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.
X
X
X
.
.
.
H
p. 138
I
p. 150
J
p. 158
.
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.
.
.
.
.
X
X
.
X
.
.
.
.
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.
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.
X
.
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.
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X
H
p. 138
I
p. 150
J
p. 158
Table 5 (cont.)
II. Observable Visit and Visitor Characteristics
(individual counts, group counts, group size, number of stock, method of travel, gender, approximate age classes,
time of entry or exit, day use vs. overnight use)
Data collection techniques
A
p. 68
B
p. 79
C
p. 90
Mechanical counters
Observer validation (accuracy)
Sample observations
Sample interviews
Visitor registration
Registration rate check
Sample interviews
Permits
Permit compliance checks
Sample interviews
Sample mailback surveys
Indirect counts
General visitor surveys
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X
X
X
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X
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Use estimation system
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p. 101 p. 110 p. 121 p. 128
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Table 5 (cont.)
III. Simple Nonobservable Visit and Visitor Characteristics
(length of stay, travel routes, sociodemographics., etc.)
Data collection techniques
A
p. 68
B
p. 79
C
p. 90
Mechanical counters
Observer validation (accuracy)
Sample interviews
Visitor registration
Registration rate check
Sample interviews
Permits
Permit compliance checks
Sample interviews
Sample mailback surveys
Indirect counts
General visitor surveys
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p. 138
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p. 150
J
p. 158
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p. 138
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p. 150
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p. 158
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p. 138
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p. 150
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p. 158
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Table 5 (cont.)
IV. Complex Nonobservable Visit and Visitor Characteristics
(visitor attitudes and preferences, perceptions of social and resource conditions, and so forth)
Data collection techniques
A
p. 68
B
p. 79
C
p. 90
Mechanical counters
Observer validation (accuracy)
Sample interviews
Visitor registration
Registration rate check
Sample interviews
Permits
Permit compliance checks
Sample interviews
Sample mailback surveys
Indirect counts
General visitor surveys
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Table 5 (cont.)
V. Summary Use Statistics
(recreation visitor-days, visitor-hours, and so forth)
Data collection techniques
A
p. 68
B
p. 79
C
p. 90
Mechanical counters
Observer validation (accuracy)
Sample observations
1 registration
Registration rate check
Sample interviews
Permits
Permit compliance checks
Sample interviews
Sample mailback surveys
Indirect counts
General visitor surveys
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
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67
System A: Mechanical Counters
With Visual Calibration
System Description ________________________________________________
This system enables the manager to obtain visit counts (individual or group
visits). Mechanical counters are set up to count trail traffic; the reliability of
counter data is assessed by simultaneous monitoring of trail traffic by either
human observers or cameras. These reliability checks (calibration) are the
key feature of the system. Because data recording and calibration are
performed without contacting visitors, there is little or no visitor burden.
Summary of System A:
Type of observations:
Measures of visitor use:
Counts
Number of individual visits
Number of group visits
Data collection strategies: Sample plan for counter rotation (if applicable)
• spatial
• temporal
Sample plan for visual calibration
Techniques/procedures:
Mechanical counters
Calibration by visual observations
• cameras
• human observers
Visitor burden:
None
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics
The use characteristics estimated with this system are limited to individual or group visit counts. Calibration determines the accuracy of the
counts; it does not provide additional data for estimating total use.
Step 2: Decide on Counter Type
There are three main types of counters currently available: photoelectric
counters, sensor pad counters, and loop-type sensor counters. Counter
selection depends on installation site, vandalism concerns, potential environmental influences on counter accuracy, equipment cost, and maintenance
requirements.
1. Installation Site.—Characteristics of the proposed installation site will
determine the type of counter that is most appropriate. Site characteristics
to be evaluated include the presence or absence of tree cover, soil type, and
68
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
slope. Photoelectric counters must be attached on a vertical surface so that
the sensor and the reflector are opposite each other and located at a distance
of 100 feet or less. If counter components are attached to trees, each tree
should be large enough to prevent excessive swaying. If there are no suitable
trees at the proposed site, posts may be installed if the soil allows digging;
however, posts must be concealed in brush to avoid vandalism. Soil type and
depth are important if sensor pads and loop-type counters are considered, as
these sensors should be buried to be operative. If digging is difficult, or the
proposed monitoring site is located on a steep or unstable surface, or both,
these counters will not be appropriate.
2. Equipment Vandalism.—Vandalism, theft, and tampering with counter
equipment are serious concerns, especially in heavy-use areas near trailheads
or parking areas. Because counter components are above ground, photoelectric counters are the most vulnerable to vandalism. Camouflaging the
equipment may prevent detection. The plastic housing of the TrailMaster
counters makes them the most susceptible to vandalism or animal damage;
the long-term durability of these counters has not been assessed. Sensor
pads are less susceptible to vandalism because they are buried, although the
counter mechanism itself must be located so that the counter display can be
read easily. The counter mechanism must therefore be camouflaged. Looptype counters are completely buried and therefore are relatively free from the
potential of damage. Avoid creating obvious trails to equipment placed off the
trails. Visitors may follow these trails out of curiosity, but this traffic may
increase the likelihood of tampering with equipment or disrupt normal
traffic flow.
3. Environmental Influences on Accuracy.—Environmental factors influencing counter accuracy include habitat structure, weather, and wildlife.
Structural factors include canopy density and substrate. For example,
counts obtained from sensor pads may be overestimated by vibration generated by swaying trees or by other ground vibrations which are not related to
visitor traffic; extremely deep or dense snow may diffuse foot traffic vibrations and bias counts upward. Count underestimates occur with photoelectric counters if the emitted beam misses the reflector, as occurs with
excessive tree sway. Wildlife passing within the detection region of passiveinfrared sensors may register a count. During rain events moisture on
receivers and reflectors may affect count accuracy.
4. Equipment Cost.—Prices vary from approximately $300 to $500 for
photoelectric and sensor pad counters to over $1,200 for loop-type counters.
Expense is increased with the inclusion of various options, such as camera
attachments. It is highly desirable that counters provide time and date
stamping of count readings; this option facilitates calibration. See table 2 for
details of equipment manufacturers, specifications, options, and associated
costs.
5. Maintenance Requirements.—Visitation of each counter station should
be performed regularly; schedules will depend on battery life, data storage
capacity, potential for equipment failure or vandalism, and counter rotation
schedules (determined before the monitoring program is in place; see below).
Data must be downloaded before batteries begin to fail, or before storage
capacity is exceeded. Battery life varies from 60 to 90 days for photoelectric
counters to over 1 year for loop-type counters. Data storage capacity is
usually much less than battery life. For example, memory capacity of loop-type
counters is limited to 40 days of hourly time-stamped data; this type of
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
69
counter would have to be visited at least this often. Memory capacity of
certain photoelectric counters may be count-limited rather than time-limited; for example, standard TrailMaster counters have a storage limit of
approximately 1000 counts. For these counters, the time between data
downloadings would depend on visitor traffic volume. Finally, the time order
and intervals of counter rotation and calibration must be scheduled.
Step 3: Decide on the Number of Counters Needed
The number of counters to acquire will be determined by the number of
access points to be monitored and the equipment budget. Ideally, mechanical
counters should be acquired for every access point. In practice, funding
limitations, the size of the wilderness area to be monitored, and relatively
large numbers of potential access points mean that the number of available
counters will be far fewer than the number required. In this case, counters
must be rotated systematically (see step 5).
Step 4: Choose the Calibration Method
Calibration is the procedure for assessing the reliability of the counting
device by comparing its output to some alternative method of known
accuracy. Calibration is performed by recording the number of individuals or
groups passing the mechanical counter during a specified observation period;
simultaneous counter readouts are obtained for the same period.
The calibration method chosen depends on:
1. The relative amount of labor and resources required for implementation.
2. The type of bias that must be estimated.
Counter output may show either overestimation bias (the counter
registers something it should not count), or underestimation bias (the
counter does not count something it should). The calibration technique
chosen should provide an accurate measure of one or both types of bias if
possible.
The two methods of calibrating counters: with cameras, or with human
observers.
1. Camera Calibration.—Cameras are installed at the traffic area where
the counter is installed; to maximize the efficiency of the method, cameras
should be set up in places where traffic will be visible for long distances. This
method minimizes the amount of personnel involvement and both types of
counter bias.
(a) Fixed-interval monitoring. All traffic during a sample period is
photographed. The camera is activated at programmed time intervals; these
intervals are selected by statistical sampling procedures.
(b) Counter-activated monitoring. The camera is attached to the counter
itself, and takes photos only when the counter is activated by visitor traffic.
This technique provides a measure of overestimation bias only; that is, it does
not provide information on errors occurring because of visitors undetected by
the counter. This strategy enables the investigator to verify group size, traffic
direction, and so forth, for visitors who actually activate the camera; blank
photos and wildlife photos enable estimates of false counts.
2. Observer Calibration.—Calibration by human observers is more labor
intensive than camera calibration, but it is more accurate. Observers should
70
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
be stationed close enough to the counter so that all traffic activating the
counter is observed; although observers need not be right on top of the
counter, they should not wander up and down the trail.
For calibration purposes, the minimum information to be recorded by
observers includes: number of individuals, number of groups, method of
travel, direction of travel, and date and time of entry or exit. Additional
information on visit or visitor characteristics may be obtained if desired; a
sample observer recording sheet is shown in figure 1. However, it must be
emphasized that observation is remote; observers do not stop visitors.
Step 5: Develop a Sampling Plan
Sampling plans must be developed for:
1. Systematic scheduling of counter rotation across trailheads (if the
number of counters does not equal the number of access points), and
2. Calibration (if observers or cameras cannot provide for continuous
calibration).
Step 6: Purchase Equipment
Table 2 gives information on counter manufacturers, equipment specifications and associated costs (1995 prices).
Step 7: Install Equipment
Specifics for site location were discussed in step 2. In general, counters
should be placed some distance away from the trailhead so that only bona fide
wilderness visitors are counted, and casual visitors (those who travel only an
extremely short distance) are excluded. However, if the wilderness boundary
is an extremely long distance from the trailhead, the increase in personnel
time involved in traveling to the counter site for reading and calibrating
counters may make this option untenable. We do not advise locating counters
where the trail is unduly wide (thus allowing visitors to travel two or more
abreast and underestimating counts), or at natural resting places (where
they may mill around and cause multiple counts). Narrow portions of the trail
at locations where traffic flow is more or less continuous offer the best count
locations.
The time required for counter installation will vary according to distance
from the trailhead and counter type. After arriving at the selected site, at
least 1 hour will be required for counter installation. This includes time spent
examining the site, selecting the best place for counter location, installing the
sensor and the counting mechanism, setting counter sensitivity or delay, and
testing counter operation. If a counter is mounted on a tree trunk (as is the
case for photoelectric counters), the counter will likely shift slightly within
the first day or two as a result of tree wounding; the counter should therefore
be checked, and realigned if necessary, on the second day after initial
installation. If cameras are used for calibration, additional time is required
to address privacy concerns (the camera must be located far enough from the
trail so that individuals cannot be identified in the pictures, camera adjusted
to be slightly out of focus, and so forth).
After the equipment has been installed, observe conditions for a short time
to make certain that the counter is functioning correctly and that any
camouflage is not obscuring or tripping the counter continuously. Walk over
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
71
the pad or through the beam several times to check counter sensitivity, and
adjust accordingly.
All equipment should be labeled with agency identification, a statement of
purpose, and the name, address, and telephone number of a designated
contact person. A message explaining that the camera is for detecting use
levels, and that individual identities cannot be determined, may reduce the
risk of vandalism if visitors do locate the equipment.
Step 8: Collect Calibration Data
Calibration information is collected according to a specific sampling strategy (as described in step 5). The specifics of collecting calibration information
will depend on whether cameras or human observers are used.
1. Camera Calibration.—Calibration observations are recorded with either motion picture (8-mm or VHS recorder) or a camera. If the camera is on
a timer, photos, or a series of frames, can be obtained at fixed intervals; the
camera can be attached to a mechanical counter and triggered to shoot by
visitor traffic. Because camera detection could result in theft or vandalism of
equipment; cameras must be positioned far enough from the trail so that
visitors cannot hear the shutter or motor action; camera equipment should
be well camouflaged. When performing routine visits, do not approach
equipment over the same route every time; frequent travel could result in the
development of a recognizable path and subsequent detection of equipment
by unauthorized persons.
Film consumption should be monitored closely; calibration data will be
useless if the camera runs out of film during this phase. After removing
exposed film from the camera, label immediately with the date, time, and
location. Protect exposed film from extreme heat and cold until developed.
Record necessary observations from the developed film; observations
include number of individuals, number of groups, date and time of entry or
exit. The method of recording observations should be standardized to minimize errors in recording. After observations are recorded, destroy negatives
and developed photos to assure visitor privacy.
2. Observer Calibration.—The observer must be stationed somewhere
near the counter where the trail is clearly visible. If trail traffic is low,
observers may perform other tasks in the vicinity of the counter, such as trail
clearance and maintenance, visitor education, or reading; these help pass the
time and reduce observer fatigue and boredom. However, if the observer is
stationed at some distance and by observing traffic through binoculars, it is
not advisable to engage in other types of activity because of the potential for
missing visitors if attention is diverted from the trail. Observers should be
in appropriate uniform and possess necessary communication and safety
equipment.
Observations must be recorded in a standardized format. For each data
sheet the observer should record his or her name, the sampling location, the
date, start time, the initial counter reading, end time, and the final counter
reading for that sample period. During the sample period the observer
records the number of individuals or groups passing the observation station,
the time of the event, and the direction of travel. The observer must be
provided with sufficient data forms for the observation period. Observers
must understand the need to completely fill out the data form; sample
observations will be useless if the data collected by the observer cannot be
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
matched with the appropriate counter data. Observation sheets should be
filed in a designated place after the observer returns to the office.
Step 9: Collect Counter Data
Counts logged by the mechanical counter are recorded at intervals determined by the sampling plan. If counters are permanently allocated to a given
location, the frequency of recording will be determined by the calibration
sampling plan. At a minimum, counts should be recorded at least twice per
month to ensure that data are not lost because of equipment malfunction.
The person obtaining count readings should check battery power and
equipment operation, and for any changes in the surrounding area which
may affect count accuracy. For example, fallen branches or trees could block
the electronic beam from the scanner, or result in the rerouting of trail traffic
away from the counter path.
Step 10: Estimate Use
Use data are collected in accordance with the desired sample size and the
sampling strategy. Because mechanical counters are the sole method of data
collection, use characteristics estimated with this system are limited to
individual or group visit counts. Use data may be expressed as a rate (for
example, number of visitors/day), or total (for example, number of visitors for
the season). In general, totals are estimated by multiplying the average daily
rate by the number of days in the time period of interest, corrected for possible
bias in estimated counts. Data collected during the calibration phase may be
used to provide estimates of the sample size required for the actual observation phase of the study.
Example. Visitor traffic in the Alpine Lakes Wilderness was studied in
1991. Measures of use were assessed at the primary trailhead access for
Snow Lake—an easily accessed high-use trail with a high concentration of
day users. The total length of the visitor season was 100 days.
1. Calibration.—The initial calibration period was 15 observation days.
The paired data used to establish the calibration relationship were as
follows:
Day
Friday
Saturday
Sunday
Wednesday
Thursday
Friday
Saturday
Sunday
Friday
Saturday
Sunday
Wednesday
Thursday
Saturday
Sunday
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Mechanical counts (X)
132
514
604
107
74
107
423
438
92
370
406
127
80
325
400
Visitors observed (Y)
119
408
556
119
74
113
424
323
78
380
356
98
87
252
361
73
The summary statistics for these data are as follows: n = 15, ΣX = 4,199,
ΣX2 = 1,643,937, ΣY = 3,748, ΣY2 = 1,294,490, ΣXY = 1,450,388, X = 280,
Y = 250. If no mechanical counters were used or if their data is ignored, the
observed data could be used to compute an estimate of total use. The mean
of the 15 observed values is 250 with a standard error of 41, making the 95
percent confidence interval 250 ± 2·41 = (167, 332). If the data is stratified
by weekends and weekdays, the estimated means and confidence intervals
are 382 (320, 445) and 98 (84, 113), respectively. Since there were 72
weekdays and 28 weekend days in the 100 day season, these individual
estimators are combined as weighted averages to make overall estimators of
17,786 (15,755, 19,817). Differences from the overall (unstratified) estimator
above may be due to an over representation of weekend days in the sample.
The mechanical counter data may be used to increase precision by estimating a regression relationship (see appendix): Y = 10.15 + 0.86·X. The standard
error of the regression equation ( MSE ) is 33.31. The R2 value is high (0.96),
suggesting that a straight line is a good approximation of the relationship
between the two variables. However, examination of the data plot (fig. 5)
shows that there are two distinct subgroups in the data. These subgroups
correspond to the day of the week on which observations were obtained;
weekends had substantially higher counts than weekdays. This suggests
that the sampling plan for the observation phase should incorporate stratification by time periods.
Because the regression slope is less than 1, the actual number of visitors
will be overestimated by the mechanical counter data. A crude estimate of the
Alpine Lakes Wilderness
Actual Counts
600
500
400
300
200
100
0
0
100 200 300 400 500 600 700
Mechanical Counts
Figure 5—Plot of visitor counts derived from a mechanical counter in comparison to those obtained from human
observers (Alpine Lakes Wilderness, 1991).
74
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Y
= 250/280 = 0.89; that
X
is, 89 percent of counts registered by the mechanical counter could be
attributed to visitor traffic, with the remaining 11 percent due to other
causes. If visitor totals are estimated for relatively long time periods, there
may be a substantial amount of accumulated error in the results. Standard
errors and confidence intervals for ratio estimators are not generally recommended and are beyond the scope of this handbook.
2. Sample Size Estimation.—Because count data are collected by mechanical counters, large sample sizes for counts are relatively easy to obtain.
However, observation data are time-intensive and expensive to collect and
process; logistically feasible sample sizes should reflect reasonable operational costs associated with equipment and personnel.
(a) Count data. The relation used to estimate sample size is:
amount of bias is given by the ratio estimator r =
S
n ≅ 4 ⋅
L
2
If the sampled population is small, the finite population correction (fpc) is
used to correct for overestimation bias. Using the fpc, the estimated sample
size is:
n≅
N ⋅ S2
L2 ⋅ N
S2 +
4(2)2
where L is the width of the interval around the projected average, and N is
the size of the true population. In this case, N is the number of days in the
season. Precision is estimated by the confidence level (generally 95 percent)
and the desired width of L. For example, the investigator may wish to be 95
percent certain that the results have a precision of ± 5 percent of the total.
Operationally feasible sample sizes are obtained by varying the amount of
precision of the estimate; highly precise estimates may require sample sizes
that are too large for practical purposes.
Example. The average number of visitors observed per day during the
calibration phase was 250, with S = 160. There are 100 days in the season (N).
Suppose we want to be 95 percent certain that results will have a precision
of ± 5 percent, or ± 13 visitors/day. The estimated number of sampling days
100(160)2
= 86. If the precision is adjusted to ± 10 percent
(13 + 13)2 (100)
2
(160) +
16
(or ± 25 visitors per day), then n = 62. Both of these are too large or too close
to the entire season of 100 days to be of practical use due to the large
underlying variance. A more reasonable level of precision would be ± 30
percent (or ± 75 visitors per day), which would call for a sample size of n = 15
as in the example above.
(b) Proportion data. Sample size (n) will be at a maximum when the
proportion of observations (p) in any given category is 0.5 (or 50 percent). The
sample size required to estimate an interval of width L around the sample
mean will be:
is ≈
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
75
n=
4 ⋅ (2)2 ⋅ p(1 − p)
L2
which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.
Example. Preliminary data showed that for 40 randomly selected visitors,
24 appeared to be day users. Therefore, the proportion of day users,
p = 24/40 = 0.60
and the standard error is p(1 − p) / n = (0.60)(0.40) / 40 = 0.0775 .
The 95 percent confidence interval based on these data is approximately 0.6 ±
2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size
n required for a 95 percent confidence interval with a length of at most 0.10
16(0.5)2
= 400.
(0.10)2
Therefore, it would be necessary to observe 400 visitors to obtain this amount
of precision for the estimate.
(c) Stratified sampling. If the data are stratified according to trailhead
or time block, sample sizes of each stratum must be calculated to ensure
accurate representation of the population. Sample sizes may be either
proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of
each strata or subgroup. Optimal allocation is a type of stratified sampling
where the sample size within each strata is proportional to both the size and
the variability of the sample within each stratum; the proportionality factor
(regardless of the resulting value of p) is approximately n =
∑
is calculated as [ Ni ⋅ Si / ( Ni ⋅ Si )] ⋅ n. Disproportional sampling occurs when
the same size sample is drawn for each stratum (assuming equal costs to
sample each strata).
Proportional sampling should be performed if strata are fairly homogeneous
(that is, the standard deviations observed for each stratum are similar), whereas
optimal allocation should be chosen if strata differ in the amount of variability.
Example. In this example, data are stratified by two time blocks—weekend
days and weekdays. This stratification strategy separates out time periods
according to relative intensity of use, with the heaviest and most variable use
occurring on weekends, and relatively light and uniform use on weekdays.
For a 100-day season, there are about 72 weekdays and 28 weekend days.
Suppose the available resources (budget, labor, time) dictated that the
maximum number of days that could be sampled was n = 25. The initial value
for the standard deviation for each stratum was estimated from the data
obtained during calibration. Sample sizes for each time block are calculated
as follows:
Proportional
fb
nc
Disproportional
f
n
Optimal
allocation
f
n
Stratum
sa
Weekends
(N1 = 28)
Weekdays
(N2 = 72)
88.0
0.25
7
0.43
12
0.64
16
19.2
0.25
18
0.17
12
0.36
9
aStandard
deviation.
proportion.
cSample size.
bSampling
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Because the two strata differ considerably in variability, the preferred
sampling scheme is optimal allocation; with this strategy the investigator
randomly selects 16 weekend days and 9 weekdays for data collection.
(3) Use Estimation.—Use characteristics estimated with this system are
limited to individual or group visit counts. Data may be expressed in terms
of: (a) the rate (for example, number of visitors per day), or (b) the total (for
example, number of visitors for the season).
(a) Rate of use. In this example the observation period was 15 days; the
counter registered a total of 4,199 counts, averaging 280 counts per day. The
calibration or regression line is used to “correct” for counter bias by using it
to estimate the “actual” value as follows:
Y = 10.15 + 0.86·(280) = 250 visitors per day.
The 95 percent confidence limits are estimated as:
250 ± 2(33.31)
(280 − 280)2
1
+
= 250 ± 17, or between 233 and
15 (1, 643, 937) − 4, 1992 / 15
267 visitors per day.
Accuracy may sometimes be increased if regressions are calculated within
each stratum rather than pooled over the entire observation period. In this
example, over 80 percent of all counts registered occurred on weekends; there
were 3,480 counts for the 8 weekend days monitored (averaging 435 counts
per day) and 719 counts for the 7 weekdays (averaging 103 counts per day).
The resulting regression estimates for each strata are as follows:
Weekend: Y = 1.71 + 0.875·(435) = 382 visitors per day, with 95 percent
confidence limits 382 ± 94, or between 288 and 476 visitors per day.
Weekday: Y = 31.1 + 0.654·(103) = 98 visitors per day, with 95 percent
confidence limits 98 ± 27, or between 72 and 125 visitors per day.
These estimators may be combined to get a “corrected” average daily total by
forming a weighted average of the individual estimates. Since there were 72
weekdays and 28 weekend days during the 100 day season, these two
estimates can be combined with weights of 72/100 and 28/100 to make an
overall estimate of visitors over the entire season. This overall estimator is
(72/100)·98 + (28/100)·382 = 178. A confidence interval for the average daily
use would be formed similarly as a weighted average of the lower and upper
confidence limits of the weekend and weekday usage rates of (132, 224).
In this example the small sample sizes and greater variability within strata
make the confidence interval for the stratified estimator much wider than
the unstratified estimator. The moral is that stratification may not always
result in narrower confidence intervals, but it will give more specific information about individual strata that may be very useful.
(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,
corrected by the estimated bias in counts. The assumption implicit in this
method is that use remains uniform over the time period of interest; if use
patterns fluctuate considerably over the season, calibration relationships
should be updated as required, and the new relationship used to calculate use
rates for that time interval.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
77
In this example, season length was 100 days. The overall visitor use
estimate is therefore 250 (100) = 25,000 visitors (23,300 to 26,700 visitors).
Using the stratified regression estimators, the total count estimates are
17,800 with a confidence interval of (13,200, 22,400).
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System B: Mechanical Counters
With Observer Calibration and
Sample Observations
System Description ________________________________________________
This system provides information on both visit counts and simple observable visit and visitor characteristics. Observable characteristics are those
which can be directly observed and need not be determined by contacting
visitors; these include group size, number of stock, method of travel, gender,
approximate age, time of entry or exit, and whether a user appears to be a day
user or an overnight camper. Mechanical counters are set up to count trail
traffic. Monitoring by either human observers or cameras is used to assess
the reliability of counter data (calibration) and obtain information on
simple observable characteristics. Because there is no visitor contact, there
is no visitor burden.
Summary of System B:
Type of observations:
Measures of visitor use:
Data collection strategies:
Techniques/procedures:
Visitor burden:
Counts
Observable characteristics
Number of individual visits
Number of group visits
Use by categories of user
Sample plan for counter rotation (if applicable)
• spatial
• temporal
Sample plan for calibration
Sample plan for observations
Mechanical counters
Visual observations (cameras, human observers)
None
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics
Direct measures of use include individual or group visit counts; mechanical
counters are used to collect count data, and count accuracy is assessed by
calibration with remote observation of actual traffic. However, additional
visit and visitor characteristics are acquired during the calibration process.
These data are simple observable characteristics which are recorded without
visitor contact; these include group size, number of stock, method of travel,
gender, approximate age, time of entry or exit, and whether a user appears
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
79
to be a day user or an overnight camper. Information on user characteristics
is used to categorize count data.
Step 2: Decide on Counter Type
There are three main types of counter currently available: photoelectric
counters, sensor pad counters, and loop-type sensor counters. Counter
selection depends on installation site, vandalism concerns, potential environmental influences on counter accuracy, equipment cost, and maintenance
requirements.
1. Installation Site.—Characteristics of the proposed installation site will
determine the type of counter that is most appropriate. Site characteristics
to be evaluated include the presence or absence of tree cover, soil type, and
slope. Photoelectric counters must be attached on a vertical surface so that
the sensor and the reflector are opposite each other and located at a distance
of 100 feet or less. If counter components are attached to trees, each tree must
be large enough to prevent excessive swaying. If there are no suitable trees
at the proposed site, posts may be installed if the soil allows digging; however,
posts should be concealed in brush to avoid vandalism. Soil type and depth
are important if sensor pads and loop-type counters are considered, as these
sensors should be buried to be operative. If digging is difficult, or the proposed
monitoring site is located on a steep or unstable surface, or both, these
counters will not be appropriate.
2. Equipment Vandalism.—Vandalism, theft, and tampering with counter
equipment are serious concerns, especially in heavy-use areas near trailheads
or parking areas. Because counter components are above ground, photoelectric counters are the most vulnerable to vandalism. Camouflaging the
equipment may prevent detection. The plastic housing of the TrailMaster
counters makes them the most susceptible to vandalism or animal damage;
the long-term durability of these counters has not been assessed. Sensor pads
are less susceptible to vandalism because they are buried, although the
counter mechanism itself must be located so that the counter display can be
read. The counter mechanism must therefore be camouflaged. Loop-type
counters are completely buried and therefore are relatively free from the
potential of damage. Avoid creating obvious trails to equipment placed off the
trails. Visitors may follow these trails out of curiosity, but this traffic may
increase the likelihood of tampering with equipment or disrupt normal
traffic flow.
3. Environmental Influences on Accuracy.—Environmental factors influencing counter accuracy include habitat structure, weather, and wildlife.
Structural factors include canopy density and substrate. For example, counts
obtained from sensor pads may be overestimated by vibration generated by
swaying trees or by other ground vibrations which are not related to visitor
traffic; extremely deep or dense snow may diffuse foot traffic vibrations and
bias counts upward. Count underestimates occur with photoelectric counters
if the emitted beam misses the reflector, as occurs with excessive tree sway.
Wildlife passing within the detection region of passive-infrared sensors may
register a count. During rain events moisture on receivers and reflectors may
affect count accuracy.
4. Equipment Cost.—Prices vary from approximately $300 to $500 for
photoelectric and sensor pad counters to over $1,200 for loop-type counters.
Expense is increased with the inclusion of various options, such as camera
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attachments. It is highly desirable that counters provide time and date
stamping of count readings; this option facilitates calibration. See table 2 for
details of equipment manufacturers, specifications, options, and associated
costs.
5. Maintenance Requirements.—Visitation of each counter station should
be performed regularly; schedules will depend on battery life, data storage
capacity, potential for equipment failure or vandalism, and counter rotation
schedules (determined before the monitoring program is in place; see
below). Data must be downloaded before batteries begin to fail, or before
storage capacity is exceeded. Battery life varies from 60 to 90 days for
photoelectric counters to over 1 year for loop-type counters. Data storage
capacity is usually much less than battery life. For example, memory
capacity of loop-type counters is limited to 40 days of hourly time-stamped
data; this type of counter would have to be visited at least this often. Memory
capacity of certain photoelectric counters may be count-limited rather than
time-limited; for example, TrailMaster counters have a storage limit of
approximately 1,000 counts. For these counters, the time between data
downloadings would depend on visitor traffic volume. Finally, counter
rotation or calibration schedules must be considered.
Step 3: Decide on the Number of Counters Needed
The number of counters to acquire will be determined by the number of
access points to be monitored and the equipment budget. Ideally, counters
should be acquired for every access point. In practice, funding limitations,
the size of the wilderness area to be monitored, and relatively large numbers
of potential access points mean that the number of available counters will
be far fewer than the number required. In this case, counters must be
rotated systematically (see step 5).
Step 4: Choose the Calibration Method
The calibration method chosen depends on the relative amount of labor
and resources required for implementation, and the type of bias that must
be estimated.
Counter output may show either overestimation bias (the counter
registers something it should not count), or underestimation bias (the
counter does not count something it should); the calibration technique
chosen should provide an accurate measure of one or both types of bias if
possible.
The two methods of calibrating counters are with cameras, and with
human observers.
1. Camera Calibration.—Strategies of camera setup will be dictated by
the relative
importance to the manager of the competing goals of labor allocation and
minimization of bias.
(a) Fixed-interval monitoring. All traffic during a sample period is
photographed. The camera is activated at programmed time intervals; these
intervals are selected by statistical sampling procedures (part I, chapter 3).
Cameras are installed at the traffic area where the counter is installed; to
maximize the efficiency of the method, cameras should be set up in places
where traffic will be visible for long distances. This method minimizes the
amount of personnel involvement and both types of counter bias.
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81
(b) Counter-activated monitoring. The camera is attached to the counter
itself, and takes photos only when the counter is activated by visitor traffic.
This technique provides a measure of overestimation bias only; it verifies
group size, traffic direction, and so forth, for visitors which actually activate
the camera, and blank photos and wildlife photos enable estimates of false
counts. This method does not provide information on errors occurring
because of visitors undetected by the counter.
2. Observer Calibration.—Calibration by human observers is more labor
intensive than camera calibration, but it is more accurate. Observers should
be stationed close enough to the counter so that all traffic activating the
counter is observed; although observers need not be right on top of the
counter, they should not wander up and down the trail.
For calibration purposes, the minimum information to be recorded by
observers includes: number of individuals, number of groups, method of
travel, direction of travel, and date and time of entry or exit. Additional
information on observable visit or visitor characteristics (for example, group
size, number of stock, gender, approximate age, time of entry or exit, and
whether a user appears to be a day user or an overnight camper) are recorded
at this time; a sample observer recording sheet is shown in figure 1. Some
information (such as gender and age categories) may not be easily determined from observations. However, it must be emphasized that observation
is remote; observers do not stop visitors.
Step 5: Develop a Sampling Plan
Sampling plans must be developed for:
1. scheduling counter rotation across trailheads on a systematic basis (if
the number of counters does not equal the number of access points).
2. calibration (if observers or cameras cannot provide for continuous
calibration).
Step 6: Purchase Equipment
Table 2 gives information on counter manufacturers, equipment specifications, and associated costs (1995 prices).
Step 7: Install Equipment
Specifics for site location were discussed in step 2. In general, counters
should be placed some distance away from the trailhead so that only bona fide
wilderness visitors are counted, and casual visitors (those who travel only an
extremely short distance) are excluded. However, if the wilderness boundary
is an extremely long distance from the trailhead, the increase in personnel
time involved in traveling to the counter site for reading and calibrating
counters may make this option untenable. We do not advise locating counters
where the trail is unduly wide (thus allowing visitors to travel two or more
abreast and underestimating counts), or at natural resting places (where
they may mill around and cause multiple counts). Narrow portions of the trail
at locations where traffic flow is more or less continuous offer the best count
locations.
The time required for counter installation will vary according to distance
from the trailhead and counter type. After arriving at the selected site, at
least 1 hour will be required for counter installation. This includes time spent
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examining the site, selecting the best place for counter location, installing the
sensor and the counting mechanism, setting counter sensitivity or delay, and
testing counter operation. If a counter is mounted on a tree trunk (as is the
case for photoelectric counters), the counter will likely shift slightly within
the first day or two as a result of tree wounding; the counter should therefore
be checked, and realigned if necessary, on the second day after initial
installation. If cameras are used for calibration, additional time is required
to address privacy concerns (the camera must be located far enough from the
trail so that individuals cannot be identified in the pictures, camera adjusted
to be slightly out of focus, and so forth).
After the equipment has been installed, observe conditions for a short time
to make certain that the counter is functioning correctly and that any
camouflage is not obscuring or tripping the counter continuously. Walk over
the pad or through the beam several times to check counter sensitivity, and
adjust accordingly.
All equipment should be labeled with agency identification, a statement of
purpose, and the name, address, and telephone number of a designated
contact person. A message explaining that the camera is for detecting use
levels, and that individual identities cannot be determined, may reduce the
risk of vandalism if visitors do locate the equipment.
Step 8: Collect Calibration Data
Calibration information is collected according to a specific plan (as described in step 5). The specifics of collecting calibration information will
depend on whether cameras or human observers are used.
1. Camera Calibration.—Calibration observations are recorded with either motion picture (8-mm or VHS recorder) or a camera. If the camera is on
a timer, photos, or a series of frames, can be obtained at fixed intervals; the
camera can be attached to a mechanical counter and triggered to shoot by
visitor traffic. Because camera detection could result in theft or vandalism of
equipment; cameras must be positioned far enough from the trail so that
visitors cannot hear the shutter or motor action; camera equipment should
be well camouflaged. When performing routine visits, do not approach
equipment over the same route every time; frequent travel could result in the
development of a recognizable path and subsequent detection of equipment
by unauthorized persons.
Film consumption should be monitored closely; calibration data will be
useless if the camera runs out of film during this phase. After removing
exposed film from the camera, label immediately with the date, time, and
location. Protect exposed film from extreme heat and cold until developed.
Record necessary observations from the developed film. Observations must
be recorded in a standardized format to minimize errors in recording.
Observations include location, date, number of individuals, number of
groups, date and time of entry or exit. Observers must understand the need
to completely and correctly fill out the data form; sample observations will be
useless if the data collected by the observer cannot be matched with the
appropriate counter data. Observation sheets should be filed in a designated
place. After observations are recorded, destroy negatives and developed
photos to ensure visitor privacy.
2. Observer Calibration.—It is essential that personnel are thoroughly
trained in the data collection procedures. Training ensures that observers
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
83
are already familiar with the research directives and the data collection
process before actual fieldwork begins. As a result, errors involved in the
learning process are reduced, and there will be greater consistency in
identifying the sampling units and recording responses. Training enables
observers to become familiar with various contingency plans, to identify
potential problems in the research directives, and to make decisions if
problems occur.
Preliminary, or pretest, fieldwork should be conducted before the actual
survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or
inadequacies in the procedures can be identified, and the consistency and
accuracy of personnel can be observed and analyzed.
Observers should be screened at intervals and their performance compared
either with each other or at different time points for the same observer;
screening provides a check on performance and identifies sources of error in
the data.
The observer must be stationed somewhere near the counter where the
trail is clearly visible. If trail traffic is low, observers may perform other tasks
in the vicinity of the counter, such as trail clearance and maintenance, visitor
education, or reading; these help pass the time and reduce observer fatigue
and boredom. However, if the observer is stationed at some distance and is
observing traffic through binoculars, it is not advisable to engage in other
types of activity because of the potential for missing visitors if attention is
diverted from the trail. Observers should be in appropriate uniform and
possess necessary communication and safety equipment.
Observations must be recorded in a standardized format. For each data
sheet the observer should record his or her name, the sampling location, the
date, start time, the initial counter reading, end time, and the final counter
reading for that sample period. During the sample period the observer
records the number of individuals or groups, the time visitors pass the
observation station, and the direction of travel. The observer must be
provided with sufficient data forms for the observation period. Observers
must understand the need to completely and correctly fill out the data form;
sample observations will be useless if the data collected by the observer
cannot be matched with the appropriate counter data. Observation sheets
should be filed in a designated place after the observer returns to the office.
Step 9: Collect Count Data
Counts logged by the mechanical counter are recorded at intervals determined by the sampling plan. If counters are permanently allocated to a given
location, the frequency of recording will be determined by the calibration
sampling plan. At a minimum, counts should be recorded at least twice per
month to ensure that data are not lost because of equipment malfunction.
The person obtaining count readings should check battery power and
equipment operation, and for any changes in the surrounding area which
may affect count accuracy. For example, fallen branches or trees could block
the electronic beam from the scanner, or result in the rerouting of trail traffic
away from the counter path.
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Step 10: Estimate Use
Use data are collected in accordance with the desired sample size and the
sampling strategy. Because data from mechanical counters are supplemented with direct observations, use can be estimated for observable categories of visitors, in addition to information on individual or group visit counts.
Use data may be expressed as a rate (for example, number of visitors per day),
or total (for example, number of visitors for the season). In general, totals are
estimated by multiplying the “corrected” average daily rate by the number
of days in the time period of interest. If observations can be classified into two
or more observable categories, the number in each category can be expressed
as a proportion or percentage of the total number of users. However, if sample
sizes are very small, proportion data are useless for evaluation purposes.
Data collected during the calibration phase may be used to provide estimates
of the sample size required for the actual observation phase of the study.
Example. Visitor traffic in the Alpine Lakes Wilderness was studied in
1991. Measures of use were assessed at the primary trailhead access for
Snow Lake—an easily accessed, high-use trail with a high concentration of
day users. The total length of the visitor season was 100 days.
1. Calibration.—The initial calibration period was 15 observation days.
The paired data used to establish the calibration relationship were as
follows:
Day
Friday
Saturday
Sunday
Wednesday
Thursday
Friday
Saturday
Sunday
Friday
Saturday
Sunday
Wednesday
Thursday
Saturday
Sunday
Mechanical counts (X)
132
514
604
107
74
107
423
438
92
370
406
127
80
325
400
Visitors observed (Y)
119
408
556
119
74
113
424
323
78
380
356
98
87
252
361
The summary statistics for these data are as follows: n = 15, ΣX = 4,199,
ΣX2 = 1,643,937, ΣY = 3,748, ΣY2 = 1,294,490, ΣXY = 1,450,388, X = 280, Y = 250.
If no mechanical counters were used or if their data is ignored, the observed
data could be used to compute an estimate of total use. The mean of the 15
observed values is 250 with a standard error of 41, making the 95 percent
confidence interval 250 ± 2·41 = (167, 332). If the data is stratified by weekends
and weekdays, the estimated means and confidence intervals are 382 (320,
445) and 98 (84, 113), respectively. Since there were 72 weekdays and 28
weekend days in the 100 day season, these individual estimators are
combined as weighted averages to make overall estimators of 17,786 (15,755,
19,817). Differences from the overall (unstratified) estimator above may be
due to an over representation of weekend days in the sample.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
85
The mechanical counter data may be used to increase precision by estimating a regression relationship: Y = 10.15 + 0.86·X ( MSE = 33.31) . The R
value is high (0.96), suggesting that a straight line is a good approximation
of the relationship between the two variables. However, examination of the
data plot (fig. 5) shows that there are two distinct subgroups in the data.
These subgroups correspond to the day of the week on which observations
were obtained; weekends had substantially higher counts than weekdays.
This suggests that the sampling plan for the observation phase should
incorporate stratification by time periods.
Because the regression slope is less than 1, the actual number of visitors
will be overestimated by mechanical counter data. A crude estimate of the
2
Y
= 250/280 = 0.89; that
X
is, 89 percent of counts registered by the mechanical counter could be
attributed to visitor traffic, with the remaining 11 percent due to other
causes. If visitor totals are estimated for relatively long time periods, there
may be a substantial amount of accumulated error in the results. Standard
errors and confidence intervals for ratio estimators are not generally recommended and are beyond the scope of this handbook.
2. Sample Size Estimation.—Because count data are collected by mechanical counters, large sample sizes for counts are relatively easy to obtain.
However, observation data are time-intensive and expensive to collect and
process; logistically feasible sample sizes should reflect reasonable operational costs associated with equipment and personnel.
amount of bias is given by the ratio estimator r =
(a) Count data. The relation used to estimate sample size is:
2
S
n ≅ 4 ⋅
L
If the sampled population is small, the finite population correction (fpc) is
used to correct for overestimation bias. Using the fpc, the estimated sample
size is:
n≅
N ⋅ S2
L2 ⋅ N
S2 +
4(2)2
where L is the width of the interval around the projected average, and N is
the size of the true population. In this case, N is the number of days in the
season. Precision is estimated by the confidence level (generally 95 percent)
and the desired width of L. For example, the investigator may wish to be 95
percent certain that the results have a precision of ± 5 percent of the total.
Operationally feasible sample sizes are obtained by varying the amount of
precision of the estimate; highly precise estimates may require sample sizes
that are too large for practical purposes.
Example. The average number of visitors observed per day during the
calibration phase was 250, with S = 160. There are 100 days in the season
(N = 100). Suppose we want to be 95 percent certain that the results will have
a precision of ± 5 percent, or ± 13 visitors/day. The estimated number of
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
100(160)2
= 86. If the precision is adjusted
(13 + 13)2 (100)
2
(160) +
16
to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these are too large
or too close to the entire season of 100 days to be of practical use due to the
large underlying variance. A more reasonable level of precision would be
± 30 percent (or ± 75 visitors per day), which would call for a sample size of
n = 15 as in the example above.
sampling days is ≈
(b) Proportion data. Sample size (n) will be at a maximum when the
proportion of observations (p) in any given category is 0.5 (or 50 percent). The
sample size required to estimate an interval of width L around the sample
mean will be:
n=
4 ⋅ (2)2 ⋅ p(1 − p)
L2
which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.
Example. Preliminary data showed that for 40 randomly selected visitors,
24 appeared to be day users. Therefore the proportion of day users, p = 24/40
= 0.60, and the standard error is
p(1 − p) / n = (0.60)(0.40) / 40 = 0.0775. The
95 percent confidence interval based on these data is approximately 0.6 ±
2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size
n required for a 95 percent confidence interval with a length of at most 0.10
16(0.5)2
= 400.
(0.10)2
Therefore, it would be necessary to observe 400 visitors to obtain this amount
of precision for the estimate.
(c) Stratified sampling. If the data are stratified according to trailhead
or time block, sample sizes of each stratum must be calculated to ensure
accurate representation of the population. Sample sizes may be either
proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of
each strata or subgroup. Optimal allocation is a type of stratified sampling
where the sample size within each strata is proportional to both the size and
the variability of the sample within each stratum; the proportionality factor
(regardless of the resulting value of p) is approximately n =
[
is calculated as Ni ⋅ Si /
∑ ( N ⋅ S )] ⋅ n. Disproportional sampling occurs when
i
i
the same size sample is drawn for each stratum (assuming equal costs to
sample each strata).
Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are
similar), whereas optimal allocation should be chosen if strata differ in the
amount of variability.
Example. In this example, data are stratified by two time blocks—
weekend days and weekdays. This stratification strategy separates out time
periods according to relative intensity of use, with the heaviest and most
variable use occurring on weekends, and relatively light and uniform use on
weekdays. For a 100-day season, there are about 72 weekdays and 28
weekend days. Suppose the available resources (budget, labor, time) dictated
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
87
that the maximum number of days that could be sampled was n = 25. The
initial value for the standard deviation for each stratum was estimated from
the data obtained during calibration. Sample sizes for each time block are
calculated as follows:
Proportional
fb
nc
Disproportional
f
n
Optimal
allocation
f
n
Stratum
sa
Weekends
(N1 = 28)
Weekdays
(N2 = 72)
88.0
0.25
7
0.43
12
0.64
16
19.2
0.25
18
0.17
12
0.36
9
aStandard
deviation.
proportion.
cSample size.
bSampling
Because the two strata differ considerably in variability, the preferred
sampling scheme is optimal allocation; with this strategy the investigator
randomly selects 16 weekend days and 9 weekdays for data collection.
3. Use Estimation.—Use characteristics estimated with this system are
limited to individual or group visit counts. Data may be expressed in terms of:
(a) the rate (for example, number of visitors per day), (b) the total (for
example, number of visitors for the season), or (c) use by category (for
example, method of travel).
(a) Rate of use. In this example the observation period was 15 days; the
counter registered a total of 4,199 counts, averaging 280 counts per day. The
calibration or regression line is used to “correct” for counter bias by using it
to estimate the “actual” value as:
Y = 10.15 + 0.86·(280) = 250 visitors per day.
The 95 percent confidence limits are estimated as:
(280 − 280)
1
+
= 250 ± 17, or between 233 and
15 (1, 643, 937) − 4, 1992 / 15
2
250 ± 2(33.31)
267 visitors per day.
Accuracy may sometimes be increased if regressions are calculated within
each stratum rather than pooled over the entire observation period. In this
example, over 80 percent of all counts registered occurred on weekends; there
were 3,480 counts for the 8 weekend days monitored (averaging 435 counts
per day) and 719 counts for the 7 weekdays (averaging 103 counts per day).
The resulting regression estimates for each strata are:
Weekend: Y = 1.71 + 0.875·(435) = 382 visitors per day, with 95 percent
confidence limits 382 ± 94, or between 288 and 476 visitors per day.
Weekday: Y = 31.1+ 0.654·(103) = 98 visitors per day, with 95 percent
confidence limits 98 ± 27, or between 72 and 125 visitors per day.
These estimators may be combined to get a “corrected” average daily total by
forming a weighted average of the individual estimates. Since there were 72
weekdays and 28 weekend days during the 100 day season, these two
estimates can be combined with weights of 72/100 and 28/100 to make an
overall estimate of visitors over the entire season. This overall estimator is
(72/100)·98 + (28/100)·382 = 178. A confidence interval for the average daily
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use would be formed similarly as a weighted average of the lower and upper
confidence limits of the weekend and weekday usage rates of (132, 224).
In this example the small sample sizes and greater variability within strata
make the confidence interval for the stratified estimator much wider than
the unstratified estimator. The moral is that stratification may not always
result in narrower confidence intervals, but it will give more specific information about individual strata that may be very useful.
(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,
corrected by the estimated bias in counts. The assumption implicit in this
method is that use remains uniform over the time period of interest; if use
patterns fluctuate considerably over the season, calibration relationships
should be updated as required, and the new relationship used to calculate use
rates for that time interval.
In this example, season length was 100 days. The overall visitor use
estimate is therefore 250(100) = 25,000 visitors (23,300 to 26,700 visitors).
Using the stratified regression estimators, the total count estimates are
17,800 with a confidence interval of (13,200, 22,400).
(c) Use by category. Frequently, visitor use is described in terms of
categories, or groups, of users; the number of users in each category is
expressed as a proportion, or percentage, of the total number of users
observed in the sample.
Example. Sample observations of method of travel (the observable visit
characteristic of interest) were made for 2,975 wilderness users. Three travel
categories were reported: hikers, horse users, and mountain bikers. Results
2
with a 95 percent confidence interval (using χ procedure based on 2 degrees
of freedom) were:
Hikers: n1 = 2,231, p1 = 2,231/2,975 = 0.75,
95% confidence interval = 0.75 ±
[
]
5.99 (0.75)(0.25) / 2, 975 = 0.75 ± 0.019 =
(0.731 to 0.769);
Horse users: n2 = 595, p2 = 595/2,975 = 0.20,
95% confidence interval = 0.20 ±
[
]
5.99 (0.20)(0.80) / 2, 975 = 0.20 ± 0.018 =
(0.18 to 0.22);
Mountain bikers: n3 = 149, p3 = 149/2,975 = 0.05,
95% confidence interval = 0.05 ±
[
]
5.99 (0.05)(0.95) / 2, 975 = 0.05 ± 0.009 =
(0.04 to 0.06).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
89
System C: Mechanical Counters
With Observer Calibration and
Sample Interviews
System Description ________________________________________________
This system provides information on visit counts, observable characteristics, and simple nonobservable characteristics. Whereas observable characteristics can be determined by observation, nonobservable characteristics
must be determined only by direct visitor contact and interviews. Simple
nonobservable characteristics include length of stay, travel routes, and
sociodemographic information. This is the only system based on mechanical
counters that can generate aggregate, or summary-use, statistics. Mechanical counters are set up to count trail traffic. Monitoring by human observers
is used to assess the reliability of counter data (calibration) and obtain
information on both observable and nonobservable characteristics. Because
there is limited visitor contact, visitor burden is low to moderate.
Summary of System C:
Type of observations:
Measures of visitor use:
Data collection strategies:
Techniques/procedures:
Visitor burden:
Counts
Observable characteristics
Simple nonobservable characteristics
Number of individual visits
Number of group visits
Use by categories of user
Summary use statistics
Sampling plan for counter rotation (if applicable)
• spatial
• temporal
Sample plan for visual calibration
Sample plan for interviews
Mechanical counters
Visual observations (human observers only)
Interviews
Moderate
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics to Measure
Mechanical counters are used to collect visitor count data; count accuracy
is assessed by calibration with data obtained from human observers.
Nonobservable visit and visitor characteristics are acquired during the
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calibration process; these data are obtained by interviewing a random
selection of visitors. To minimize visitor burden, only simple nonobservable
characteristics are recorded; these include length of stay, group size, wilderness travel patterns, visitor residence, visit frequency, activities, and visitor
perception of problems, resource conditions, and so forth. Use, in terms of
number of visitors, is usually categorized by one or more nonobservable
characteristics.
Step 2: Decide on Counter Type
There are three main types of counter currently available: photoelectric
counters, sensor pad counters, and loop-type sensor counters. Counter
selection depends on installation site characteristics and limitations, vandalism concerns, environmental factors affecting counter accuracy, equipment cost, and maintenance requirements.
1. Installation Site.—Characteristics of the proposed installation site will
determine the type of counter that is most appropriate. Site characteristics
to be evaluated include the presence or absence of tree cover, soil type, and
slope. Photoelectric counters must be attached on a vertical surface so that
the sensor and the reflector are opposite each other and located at a distance
of 100 feet or less. If counter components are attached to trees, each tree must
be large enough to prevent excessive swaying. If there are no suitable trees
at the proposed site, posts may be installed if the soil allows digging; however,
posts should be concealed in brush to avoid vandalism. Soil type and depth
are important if sensor pads and loop-type counters are considered, as these
sensors must be buried to be operative. If digging is difficult, or the proposed
monitoring site is located on a steep and/or unstable surface, these counters
will not be appropriate.
2. Equipment Vandalism.—Vandalism, theft, and tampering with counter
equipment are serious concerns, especially in heavy-use areas near trailheads
or parking areas. Because counter components are above ground, photoelectric counters are the most vulnerable to vandalism. Camouflaging the
equipment may prevent detection. The plastic housing of the TrailMaster
counters makes them the most susceptible to vandalism or animal damage;
the long-term durability of these counters has not been assessed. Sensor pads
are less susceptible to vandalism because they are buried, although the
counter mechanism itself must be located so that the counter display can be
read. The counter mechanism must therefore be camouflaged. Loop-type
counters are completely buried and therefore are relatively free from the
potential of damage. Avoid creating obvious trails to equipment placed off the
trails. Visitors may follow these trails out of curiosity, but this traffic may
increase the likelihood of tampering with equipment or disrupt normal
traffic flow.
3. Environmental Factors.—Environmental factors influencing counter
accuracy include habitat structure, weather, and wildlife. Structural factors
include canopy density and substrate. For example, counts obtained from
sensor pads may be overestimated by vibration generated by swaying trees
or by other ground vibrations which are not related to visitor traffic;
extremely deep or dense snow may diffuse foot traffic vibrations and bias
counts upward. Count underestimates occur with photoelectric counters if
the emitted beam misses the reflector, as occurs with excessive tree sway.
Wildlife passing within the detection region of passive-infrared sensors may
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
91
register a count. During rain events moisture on receivers and reflectors may
affect count accuracy.
4. Equipment Cost.—Prices vary from approximately $300 to $500 for
photoelectric and sensor pad counters to over $1200 for loop-type counters.
Expense is increased with the inclusion of various options, such as camera
attachments. It is highly desirable that counters provide time and date
stamping of count readings; this option facilitates calibration. See table 2 for
details of equipment manufacturers, specifications, options, and associated
costs.
5. Maintenance Requirements.—Visitation of each counter station should
be performed regularly; schedules will depend on battery life, data storage
capacity, potential for equipment failure or vandalism, and counter rotation
schedules (determined before the monitoring program is in place; see below).
Data must be downloaded before batteries begin to fail, or before storage
capacity is exceeded. Battery life varies from 60 to 90 days for photoelectric
counters to over 1 year for loop-type counters. Data storage capacity is
usually much less than battery life. For example, memory capacity of looptype counters is limited to 40 days of hourly time-stamped data; this type of
counter would have to be visited at least this often. Memory capacity of
certain photoelectric counters may be count-limited rather than time-limited; for example, TrailMaster counters have a storage limit of approximately
1000 counts. For these counters, the time between data downloadings would
depend on visitor traffic volume. Finally, counter rotation or calibration
schedules must be considered.
Step 3: Decide on the Number of Counters Needed
The number of counters to acquire will be determined by the number of
access points to be monitored and the equipment budget. Ideally, counters
should be acquired for every access point. In practice, funding limitations,
the size of the wilderness area to be monitored, and relatively large numbers
of potential access points mean that the number of available counters will be
far fewer than the number required. In this case, counters must be rotated
systematically (see step 5).
Step 4: Develop a Sampling Plan
Sampling plans must be developed for:
1. scheduling counter rotation across trailheads on a systematic basis (if
the number of counters does not equal the number of access points).
2. calibration (if continuous calibration by observers cannot be provided).
3. visitor selection for interviews.
Step 5: Purchase Equipment
Table 2 gives information on counter manufacturers, equipment specifications, and associated costs (1995 prices).
Step 6: Install Equipment
Specifics for site location were discussed in step 2. In general, counters
should be placed some distance away from the trailhead so that only bona fide
wilderness visitors are counted, and casual visitors (those who travel only an
extremely short distance) are excluded. However, if the wilderness boundary
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is an extremely long distance from the trailhead, the increase in personnel
time involved in traveling to the counter site for reading and calibrating
counters may make this option untenable. We do not advise locating counters
where the trail is unduly wide (thus allowing visitors to travel two or more
abreast and underestimating counts), or at natural resting places (where
they may mill around and cause multiple counts). Narrow portions of the trail
at locations where traffic flow is more or less continuous offer the best count
locations.
The length of time required for counter installation will vary according to
distance from the trailhead and counter type. After arriving at the selected
site, at least 1 hour will be required for counter installation. This includes
time spent examining the site, selecting the best place for counter location,
installing the sensor and the counting mechanism, setting counter sensitivity or delay, and testing counter operation. If a counter is mounted on a tree
trunk (as is the case for photoelectric counters), the counter will likely shift
slightly within the first day or two as a result of tree wounding; the counter
should therefore be checked, and realigned if necessary, on the second day
after initial installation.
After the equipment has been installed, observe conditions for a short time
to make certain that the counter is functioning correctly and that any
camouflage is not obscuring or tripping the counter continuously. Walk over
the pad or through the beam several times to check counter sensitivity, and
adjust accordingly.
All equipment should be labeled with agency identification, a statement of
purpose, and the name, address, and telephone number of a designated
contact person.
Step 7: Collect Counter Data
Counts logged by the mechanical counter are recorded at intervals determined by the sampling plan. If counters are permanently allocated to a given
location, the frequency of recording will be determined by the calibration
sampling plan. At a minimum, counts should be recorded at least twice per
month to ensure that data are not lost because of equipment malfunction.
The person obtaining count readings should check battery power and
equipment operation, and for any changes in the surrounding area which
may affect count accuracy. For example, fallen branches or trees could block
the electronic beam from the scanner, or cause a sufficient barrier to trail
traffic to reroute traffic away from the counter path.
Step 8: Select and Train the Interview Team
Careful selection and training of the personnel who are involved in
collecting data are essential if the manager or research planner is not
performing the field research. The research planner must ensure that
interviews are conducted and observations collected in the manner required
by the study plan.
1. Personnel Selection.—Both personality and ability must be evaluated
in the selection process. The importance of visitor contact extends beyond the
quality of data obtained; it is an opportunity to present the image of the
managing agency. Select an interviewer who is friendly, reliable, knowledgeable, flexible, and who demonstrates a positive attitude toward the project.
Personnel who are convinced of the value of the work will bring a sense of
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
93
commitment to the job regardless of the amount of pay or hours worked;
negative attitudes toward the overall objectives of the project, the interview
topic, or the public will jeopardize research results. Personnel should be
familiar with the wilderness area and be prepared to handle requests for
information about the wilderness and the surrounding area. Many of the
questions from visitors will not be related to the interview; providing
information is a courtesy which contributes to establishing rapport with the
visitors and increases visitor cooperation. Personnel should be trained in
emergency procedures. When in the field, personnel should be in appropriate
uniform and possess necessary communication and safety equipment.
2. Training.—It is essential that personnel are thoroughly trained in the
data collection procedures. Training ensures that observers are familiar with
the research directives and the interviewing process before actual fieldwork
begins. As a result, errors involved in the learning process are reduced, and
there will be greater consistency in identifying the sampling units (in this
case visitors to be interviewed) and recording responses. Training enables
observers to become familiar with various contingency plans, to identify
potential problems in the research directives, and to make decisions if
problems occur.
Preliminary, or pretest, fieldwork should be conducted before the actual
survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or
inadequacies in the procedures can be identified and eliminated, and the
consistency and accuracy of personnel can be observed and analyzed.
Observers should be screened at intervals and their performance compared
either with each other or at different time points for the same observer;
screening provides a check on performance and identifies sources of error in
the data.
Step 9: Collect Calibration and Interview Data
Counter calibration and interview data are collected simultaneously by
observers. Both calibration and interview information are collected according to a specific plan (as described in step 4). The observer must be provided
with sufficient research material for the observation period; these materials
include question sheets, data forms, field coding keys, writing tools, and
sampling schedules.
Observers must understand the need to completely and correctly fill out the
data form; sample observations will be useless if the data collected by the
observer cannot be matched with the appropriate counter data. Observation
sheets should be filed in a designated place after the observer returns to the
office.
1. Calibration Data.—Calibration observations must be recorded in a
standardized format. For each data sheet, the observer should record his or
her name, the sampling location, the date, start time, the initial counter
reading, end time, and the final counter reading for that sample period.
During the sample period, the observer records the number of individuals or
groups, the time visitors pass the observation station, and the direction of
travel.
2. Interview Data.—The interview protocol consists of four steps: (a)
determining question format, (b) obtaining OMB-clearance, (c) visitor selection, and (d) data collection.
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(a) Question format. The questions asked of the visitor will be dictated
on the basis of the study objectives; that is, on the basis of what the manager
wants to know and why. Questions should be easily understood by the visitor,
they should not be too long, and there should not be too many of them. Ask
only the questions necessary to meet the study objectives, and no more. For
example, suppose the manager is interested in evaluating relative impact in
terms of time spent in different areas by various user groups. Interviews can
be limited to determining method of travel, destination, and length of stay of
visitors encountered at each trailhead; the interview will be short.
Do not add questions merely to fill up space on the interview sheet. If some
inadequacy or ambiguity becomes apparent with the set questions, clarifying
questions may be added, but only if they satisfy the requirements of step 1.
The question designer is rarely a good judge of the clarity of the questions
(Ackoff 1953); preliminary field tests are invaluable for identifying problems
before the actual field surveys begin.
(b) Obtain OMB-clearance. According to federal legislation, clearance
from the Office of Management and Budget (OMB) is required if federal
employees ask more than nine members of the public the same set of
questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the
Forest Service, application for clearance is submitted to that Agency’s
Information Systems office in Washington, DC, which then forwards the
application to the Department of Agriculture, and from there to OMB for
final approval. The time from initial submission to final OMB clearance is
usually about 3 months.
(c) Interview selection. Visitors are selected in accordance with the
predetermined sampling plan (step 4). The location of interviews will be
determined by study objectives; visitors may be interviewed upon either
entry or exit, or both. For example, if the emphasis of the study is on the
effects of group size or place of residence on wilderness use, these factors are
unaffected by interview location. However, if the study objectives require
information on patterns of visitor use within the wilderness area (for
example, travel or camping locations, length of stay), visitors should be
interviewed as they leave.
(d) Data collection. When interviewing visitors, personnel should begin
with a standard introduction. Personnel should give their name and agency
affiliation and the reason for the interview. For example, “Hello, I am
Marilyn Holgate. I work for the Missoula District of the Lolo National Forest.
We are trying to learn more about the use of the Rattlesnake Wilderness. It
will help us with management of the area. May I ask you a few questions
about your visit today?” After the interview, thank visitors for their time.
Personnel may be tempted to add additional questions “just out of curiosity”;
this cannot be justified in any circumstances.
Responses should be recorded as they are given; interviewers should not
rely on memory to fill in the interview sheet at a later time. Make sure every
item is complete and legible; data forms must include date, time, location,
and interviewer’s name. When interview responses are coded, the interviewer should be provided with a field coding key to ensure that responses are
entered correctly. Completed data forms should be filed in a safe place.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
95
Step 10: Estimate Use
Use data are collected in accordance with the desired sample size and the
sampling strategy. Because data from mechanical counters are supplemented with direct observations, use can be estimated for observable categories of visitor, in addition to information on individual or group visit counts.
Use data may be expressed as a rate (for example, number of visitors per day),
or total (for example, number of visitors for the season). In general, totals are
estimated by multiplying the “corrected” average daily rate by the number
of days in the time period of interest. If observations can be classified into two
or more observable categories, the number in each category can be expressed
as a proportion or percentage of the total number of users. However, if sample
sizes are very small, proportion data are useless for evaluation purposes.
Data collected during the calibration phase may be used to provide estimates
of the sample size required for the actual observation phase of the study.
Example. Visitor traffic in the Alpine Lakes Wilderness was studied in
1991. Measures of use were assessed at the primary trailhead access for
Snow Lake—an easily accessed, high-use trail with a high concentration of
day users. The total length of the visitor season was 100 days.
1. Calibration.—The initial calibration period was 15 observation days.
The paired data used to establish the calibration relationship were as
follows:
Day
Friday
Saturday
Sunday
Wednesday
Thursday
Friday
Saturday
Sunday
Friday
Saturday
Sunday
Wednesday
Thursday
Saturday
Sunday
Mechanical counts (X)
132
514
604
107
74
107
423
438
92
370
406
127
80
325
400
Visitors observed (Y)
119
408
556
119
74
113
424
323
78
380
356
98
87
252
361
The summary statistics for these data are as follows: n = 15, ΣX = 4,199,
ΣX2 = 1,643,937, ΣY = 3,748, ΣY2 = 1,294,490, ΣXY = 1,450,388, X = 280, Y = 250.
If no mechanical counters were used or if their data is ignored, the observed
data could be used to compute an estimate of total use. The mean of the 15
observed values is 250 with a standard error of 41, making the 95 percent
confidence interval 250 ± 2·41 = (167, 332). If the data is stratified by
weekends and weekdays, the estimated means and confidence intervals are
382 (320, 445) and 98 (84, 113), respectively. Since there were 72 weekdays
and 28 weekend days in the 100 day season, these individual estimators are
combined as weighted averages to make overall estimators of 17,786 (15,755,
19,817). Differences from the overall (unstratified) estimator above may be
due to an over representation of weekend days in the sample.
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The mechanical counter data may be used to increase precision by estimating a regression relationship: Y = 10.15 + 0.86·X ( MSE = 33.31) . The R
value is high (0.96), suggesting that a straight line is a good approximation
of the relationship between the two variables. However, examination of the
data plot (fig. 5) shows that there are two distinct subgroups in the data.
These subgroups correspond to the day of the week on which observations
were obtained; weekends had substantially higher counts than weekdays.
This suggests that the sampling plan for the observation phase should
incorporate stratification by time periods.
Because the regression slope is less than 1, the actual number of visitors
will be overestimated by the mechanical counter data. A crude estimate of the
amount of bias is given by the ratio estimator r = Y / X = 250/280 = 0.89; that
is, 89 percent of counts registered by the mechanical counter could be
attributed to visitor traffic, with the remaining 11 percent due to other
causes. If visitor totals are estimated for relatively long time periods, there
may be a substantial amount of accumulated error in the results. Standard
errors and confidence intervals for ratio estimators are not generally recommended and are beyond the scope of this handbook.
2. Sample Size Estimation.—Because count data are collected by mechanical counters, large sample sizes for counts are relatively easy to obtain.
However, observation data are time-intensive and expensive to collect and
process; logistically feasible sample sizes should reflect reasonable operational costs associated with equipment and personnel.
(a) Count data. The relation used to estimate sample size is:
S
n ≅ 4 ⋅
L
2
If the sampled population is small, the finite population correction (fpc) is
used to correct for overestimation bias. Using the fpc, the estimated sample
size is:
n≅
N ⋅ S2
L2 ⋅ N
S2 +
4(2) 2
where L is the width of the interval around the projected average, and N is
the size of the true population. In this case, N is the number of days in the
season. Precision is estimated by the confidence level (generally 95 percent)
and the desired width of L. For example, the investigator may wish to be 95
percent certain that the results have a precision of ± 5 percent of the total.
Operationally feasible sample sizes are obtained by varying the amount of
precision of the estimate; highly precise estimates may require sample sizes
that are too large for practical purposes.
Example. The average number of visitors observed per day during the
calibration phase was 250, with S = 160. There are 100 days in the season
(N = 100). Suppose we want to be 95 percent certain that results will have a
precision of ± 5 percent, or ± 13 visitors/day. The estimated number of
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
97
100(160)2
= 86. If the precision is adjusted
2
(
)
(
)
13
+
13
100
(160)2 +
16
to ± 10 percent (or ± 25), then n = 62. Both of these are too large or too close
to the entire season of 100 days to be of practical use due to the large
underlying variance. A more reasonable level of precision would be ± 30
percent (or ± 75 visitors per day), which would call for a sample size of n = 15
as in the example above.
(b) Proportion data. Sample size (n) will be at a maximum when the
proportion of observations (p) in any given category is 0.5 (or 50 percent). The
sample size required to estimate an interval of width L around the sample
mean will be:
sampling days is ≈
n=
4 ⋅ (2)2 ⋅ p(1 − p)
L2
which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.
Example. Preliminary data showed that for 40 randomly selected
visitors, 24 appeared to be day users. Therefore, the proportion of day users,
p = 24/40 = 0.60, and the standard error is p(1 − p) / n = (0.60)(0.40) / 40 =
0.0775. The 95 percent confidence interval based on these data is approximately 0.6 ± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The
sample size n required for a 95 percent confidence interval with a length of
at most 0.10 (regardless of the resulting value of p) is approximately
16(0.5)2
= 400. Therefore, it would be necessary to observe 400 visitors
(0.10)2
to obtain this amount of precision for the estimate.
(c) Stratified sampling. If the data are stratified according to trailhead
or time block, sample sizes of each stratum must be calculated to ensure
accurate representation of the population. Sample sizes may be either
proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of
each strata or subgroup. Optimal allocation is a type of stratified sampling
where the sample size within each strata is proportional to both the size and
the variability of the sample within each stratum; the proportionality factor
n=
[
is calculated as Ni ⋅ Si /
∑ ( N ⋅ S )] ⋅ n. Disproportional sampling occurs when
i
i
the same size sample is drawn for each stratum (assuming equal costs to
sample each strata).
Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are
similar), whereas optimal allocation should be chosen if strata differ in the
amount of variability.
Example. In this example, data are stratified by two time blocks—
weekend days and weekdays. This stratification strategy separates out time
periods according to relative intensity of use, with the heaviest and most
variable use occurring on weekends, and relatively light and uniform use on
weekdays. For a 100-day season, there are about 72 weekdays and 28
weekend days. Suppose the available resources (budget, labor, time) dictated
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
that maximum number of days that could be sampled was n = 25. The initial
value for the standard deviation for each stratum was estimated from the
data obtained during calibration. Sample sizes for each time block are
calculated as follows:
Proportional
fb
nc
Disproportional
f
n
Optimal
allocation
f
n
Stratum
sa
Weekends
(n1 = 28)
Weekdays
(n2 = 72)
88.0
0.25
7
0.43
12
0.64
16
19.2
0.25
18
0.17
12
0.36
9
aStandard
deviation.
proportion.
cSample size.
bSampling
Because the two strata differ considerably in variability, the preferred
sampling scheme is optimal allocation; with this strategy, the investigator
randomly selects 16 weekend days and 9 weekdays for data collection.
3. Use Estimation.—Use characteristics estimated with this system are
limited to individual or group visit counts. Data may be expressed in terms of:
(a) the rate (for example, number of visitors per day), (b) the total (for
example, number of visitors for the season), (c) use by category (for example,
cooking method), or (d) use description (for example, length of stay).
(a) Rate of use. In this example, the observation period was 15 days; the
counter registered a total of 4,199 counts, averaging 280 counts per day. The
calibration or regression line is used to “correct” for counter bias by using it
to estimate the “actual” value as:
Y = 10.15 + 0.86·(280) = 250 visitors per day.
The 95 percent confidence limits are estimated as:
(280 − 280)
1
+
= 250 ± 17, or between 233 and
15 (1, 643, 937) − 4, 1992 / 15
2
250 ± 2(33.31)
267 visitors per day.
Accuracy may sometimes be increased if regressions are calculated within
each stratum, rather than pooled over the entire observation period. In this
example, over 80 percent of all counts registered occurred on weekends; there
were 3,480 counts for the 8 weekend days monitored (averaging 435 counts
per day) and 719 counts for the 7 weekdays (averaging 103 counts per day).
The resulting regression estimates for each strata are:
Weekend: Y = 1.71 + 0.875·(435) = 382 visitors per day, with 95 percent
confidence limits 382 ± 94, or between 288 and 476 visitors per day.
Weekday: Y = 31.1 + 0.654·(103) = 98 visitors per day, with 95 percent
confidence limits 98 ± 27, or between 72 and 125 visitors per day.
These estimators may be combined to get a “corrected” average daily total by
forming a weighted average of the individual estimates. Since there were 72
weekdays and 28 weekend days during the 100 day season, these two
estimates can be combined with weights of 72/100 and 28/100 to make an
overall estimate of visitors over the entire season. This overall estimator is
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
99
(72/100)·98 + (28/100)·382 = 178. A confidence interval for the average daily
use would be formed similarly as a weighted average of the lower and upper
confidence limits of the weekend and weekday usage rates of (132, 224).
In this example, the small sample sizes and greater variability within
strata make the confidence interval for the stratified estimator much wider
than the unstratified estimator. The moral is that stratification may not
always result in narrower confidence intervals, but it will give more specific
information about individual strata that may be very useful.
(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,
corrected by the estimated bias in counts. The assumption implicit in this
method is that use remains uniform over the time period of interest; if use
patterns fluctuate considerably over the season, calibration relationships
should be updated as required, and the new relationship used to calculate use
rates for that time interval.
In this example, season length was 100 days. The overall visitor use
estimate is therefore 250(100) = 25,000 visitors (23,300 to 26,700 visitors).
Using the stratified regression estimators, the total count estimates are
17,800 with a confidence interval of (13,200, 22,400).
(c) Use by category. Frequently, visitor use is described in terms of
categories, or groups, of users; the number of users in each category is
expressed as a proportion, or percentage, of the total number of users in the
sample.
Example. Sample interviews recorded three types of cooking methods:
stoves, wood fires, and neither for 2,975 wilderness users. Results with a 95
percent confidence interval (using χ2 procedure based on 2 degrees of
freedom) were:
Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,
95% confidence interval = 0.75 ±
[
]
5.99 (0.75)(0.25) / 2, 975 = 0.75 ± 0.019 =
(0.731 to 0.769);
Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,
95% confidence interval = 0.20 ±
[
]
5.99 (0.20)(0.80) / 2, 975 = 0.20 ± 0.018 =
(0.18 to 0.22);
Neither: n3 = 149, p3 = 149/2,975 = 0.05,
95% confidence interval = 0.05 ±
[
]
5.99 (0.05)(0.95) / 2, 975 = 0.05 ± 0.009 =
(0.04 to 0.06).
(d) Use description. One variable that may be obtained by interview is
information on length of stay. Post stratification may also be of interest.
Example. A sample of 38 interviews had an average length of stay of 2.4
nights with a standard error of 0.23 nights. This makes the 95 percent
confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.84, 2.76).
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System D: Visitor Registration
System With Checks For
Registration Rate
System Description ________________________________________________
This system provides information on visit counts, observable visit and
visitor characteristics, and some simple nonobservable visit characteristics.
In general, visitors fill out survey cards before entering the wilderness area,
and use characteristics are obtained from the resulting information. Registration is voluntary; the accuracy of registration data must be determined by
estimating actual registration rates, or compliance. Compliance rates are
determined by sensor-triggered cameras, or by human observers. Visitor
burden is low to moderate, and involves the time required by the visitor to
complete the registration form.
Summary of System D:
Type of observations:
Measures of visitor use:
Data collection strategies:
Techniques/procedures:
Visitor burden:
Counts
Observable characteristics
Simple nonobservable characteristics
Number of individual visits
Number of group visits
Use by categories of user
Sampling plan for station rotation (if applicable)
• spatial
• temporal
Sampling plan for compliance (cameras,
humans)
Voluntary visitor registration
Compliance checks
• human observers
• cameras
Low to moderate
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics to Measure
Direct measures of use include individual or group visit counts. Additional
visit characteristics acquired from the registration cards include length of
stay, entry and exit points, method of travel, group size, number of stock, and
place of residence (applicable to the party leader only).
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101
Step 2: Decide on Registration Form
Standard OMB-approved registration forms are available. Alternatively,
customized registration forms can be used; however, OMB clearance must be
obtained for new forms before the study begins. According to federal legislation, OMB clearance is required if federal employees ask more than nine
members of the public the same set of questions. The proposed set of
questions, methodology, and study justification must be submitted to OMB
through the appropriate channels. For the Forest Service, application for
clearance is submitted to Information Systems in Washington, DC, which
forwards the application to the Department of Agriculture, and from there to
OMB for final approval. The time from initial submission to final OMB
clearance is usually about 3 months.
“Diary”-type registration cards can give more complete information on
wilderness experiences of visitors. Visitors complete the initial portion of the
card upon entry; this section requests basic information on the visitors or
group. The second portion requests information on the trip itself, and is filled
out by the visitor during the trip, or upon leaving the wilderness area. To
reduce error, the two sections should be distinguished by separate headings
and by different colors; however, each section should have the same identification number to allow matching after collection.
Step 3: Decide on Number of Registration Stations
Registration stations are relatively inexpensive to construct, install, and
maintain. However, stations must be kept supplied with adequate amounts
of registration forms and pencils at all times. The image of the agency suffers
if visitors are prevented from registering because supplies are lacking.
Therefore, registration stations should not be placed on every trail if
personnel and time are limited and stations cannot be monitored on a regular
basis. It is preferable to have only the number of registration stations that
can be conveniently monitored and supplied.
Coverage of the wilderness area is performed by alternating “in-use”
stations across trailheads. Strategies for rotation schedules are given in step 5.
Step 4: Decide on Method of Estimating Registration Rates
Because registration is voluntary and there are no penalties for noncompliance, the number of visitors who do register may be highly variable. Factors
affecting registration rates include method of travel (hikers register at a
higher rate than horse riders do), group size (at least one member from a large
group is more likely to register than a member of a small group), and the
location of the registration station (registration rates are lower if located at
the trailhead entrance than those located further up the trail). However,
there is an unknown relationship between visitor characteristics and the
likelihood that a given group will register. Therefore, for practical purposes,
registration stations may be regarded as a type of counter; supplementary
observations must be made to estimate registration rates and “calibrate”
registration information in much the same manner as observations were
used to calibrate mechanical counters. Basic options for determining registration rates include use of cameras or human observers.
1. Cameras.—Either a video camera with VHS recorder or a camera may
be used for recording observations. If the camera is on a timer, photos (or a
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series of frames) can be obtained at fixed intervals (fixed-interval monitoring). Alternatively, the camera can be attached to a mechanical counter and
triggered to shoot by visitor traffic (counter-activated monitoring).
(a) Fixed-interval monitoring. This method requires a minimum amount
of personnel involvement. All traffic during a sample period is photographed.
The camera is activated at programmed time intervals; these intervals are
selected by statistical sampling procedures (part I, chapter 3). Cameras are
installed on the traffic area where the registration station is installed. To
maximize the efficiency of the method, cameras must be set up near the
registration station where traffic will be visible for long distances.
(b) Counter-activated monitoring. The camera is attached to a mechanical counter, and takes photos only when the counter is activated by visitor
traffic. This technique provides a measure of overestimation bias only; it does
not provide information on error occurring because of visitors undetected by
the counter.
2. Observers.—Estimating registration rates with observations taken by
human observers is more labor intensive than use of cameras, but it is more
accurate. Observers should be stationed close enough to the registration
station so that all traffic activating the counter is observed; although
observers need not be exactly by the registration station, they should not
wander up and down the trail. However, it must be emphasized that
observation is remote; observers do not stop visitors.
Step 5: Develop a Sampling Plan
Sampling plans must be developed for scheduling:
1. the rotation of registration stations and cameras (if applicable) across
trailheads.
2. observer monitoring (if continuous compliance checks are not possible).
Registration stations are not expensive to construct, install, or maintain.
However, if labor or supplies (such as cameras) are insufficient for all
trailheads, registration stations must be rotated on a systematic basis.
Step 6: Purchase Equipment
If registration rates are estimated by camera, appropriate equipment
(cameras, film, mechanical counters) must be obtained from the relevant
suppliers (see part I, chapter 2, for details of counter specifications and
manufacturers).
Step 7: Construct the Registration Stations
Registration rates are greatly affected by station design. Visitors are more
likely to stop and register if the station is both attractive and functional.
Registration stations should be designed to provide (1) a place for supplies
(pencils and registration forms), (2) a convenient, solid writing surface for the
visitor to use when completing the registration form, and (3) a place to deposit
completed forms (normally a slot at the front). Registration stations may be
constructed of wood or metal, and should be set on a post at a convenient
height. Instructions must be provided which clearly detail (1) who is to
register (one person or everyone in the group), (2) when to register (upon
entry or exit), and (3) where to deposit the completed registration form.
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103
A well-designed, easy-to-read, and attractive sign has the dual purpose of
gaining the attention of the visitor and providing relevant information. The
ideal sign is characterized by high-quality artwork depicting different types
of users (hikers and stock users, and male and female users). The accompanying message should provide clear instructions for the visitor, as well as a
brief explanation of management’s intended use of the information provided
(for example, use estimation, planning maintenance activities, and so forth).
Step 8: Install Equipment
Registration stations are installed as required. Optional equipment installation includes camera setup for registration rate estimation.
1. Registration Stations.—Registration rates are affected by station location. Do not establish registration stations at the trailhead or at parking
areas; registration rates are higher and vandalism is reduced if stations are
located at least one-quarter to 1 mile along the trail. However, if possible,
registration stations should be outside the wilderness boundary. The registration station should be clearly visible from a distance; this is particularly
important in stock-use areas, as horse users need to plan ahead for a stop.
The location site must have sufficient room to allow parties leaving the area
to pass a registering party, and allow members of the group the opportunity
to stop and rest while the designated member registers.
In general, horse users register at much lower rates than hikers do; this is
partly the result of the logistic problems associated with managing pack
strings. Some experimentation with station location may be necessary to
achieve acceptable horse-user registration rates. For example, registration
stations may be located at designated or natural stock loading/unloading
areas, where stock users can register before moving the stock out on the trail.
2. Camera Installation (optional).—When cameras are used to estimate
registration rates, they must be properly placed and maintained if the
resulting observations are to be usable. The camera must be positioned so
that group numbers, the presence of stock and camping gear, and so forth,
can be determined; however, because of privacy concerns, individual identities should not be discernible. The camera should be adjusted to be slightly
out of focus. Cameras must be positioned far enough from the trail so that
visitors cannot hear the shutter or motor action (camera detection could
result in theft or vandalism of equipment); camera equipment should be well
camouflaged.
All equipment should be labeled with agency identification, a statement of
purpose, and the name, address and telephone number of a designated
contact person.
Film consumption should be monitored frequently; registration rates
cannot be estimated if the camera runs out of film during this phase. After
removing exposed film from the camera, label immediately with the date,
time, and location. Protect exposed film from extreme heat and cold until
developed.
Counter-activated cameras: If mechanical counters are used to trigger the
camera, extra time and labor are required for installation. Specifics for
counter site location were discussed in detail for System C, step 2. In general,
mechanical counters should be placed some distance away from the trailhead
so that only bona fide wilderness visitors are counted, and casual visitors
(those who travel only an extremely short distance) are excluded. However,
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if the wilderness boundary is an extremely long distance from the trailhead,
the increase in personnel time involved in traveling to the counter site for
reading and calibrating counters may make this option untenable. Do not
locate counters and counter-activated cameras at the registration station
itself; group members tend to mill around while one member is registering,
and this will cause multiple counts. The counter sensor and camera should
be placed a short distance beyond the registration station to ensure that all
visitors pass the registration station.
The time required for counter installation will vary according to distance
from the trailhead and counter type. After arriving at the selected site, at
least 1 hour will be required for counter installation. This includes time spent
examining the site, selecting the best place for counter location, installing the
sensor and the counting mechanism, setting counter sensitivity or delay, and
testing counter operation. If a counter is mounted on a tree trunk (as is the
case for photoelectric counters), the counter will likely shift slightly within
the first day or two as a result of tree wounding; the counter should therefore
be checked, and realigned if necessary, on the second day after initial
installation.
After the equipment has been installed, observe conditions for a short time
to make certain that the counter is functioning correctly and that any
camouflage is not obscuring or tripping the counter continuously. Walk over
the pad or through the beam several times to check counter sensitivity, and
adjust accordingly.
Step 9: Collect Registration Data
Completed registration cards should be collected on a regular basis. The
person collecting the cards should check the station supplies (unused registration cards and pencils), and replenish if necessary. Keep track of the
number of unused cards in order to assess whether the time intervals for
station visits are appropriate; obviously stations will have to be visited more
frequently if the supply of unused cards runs out before each scheduled
supply drop.
Step 10: Obtain Registration Rate Data
To estimate registration rates, the minimum information required includes number of individuals, number of groups, method of travel, and date
and time of entry or exit. Additional information on observable visit or visitor
characteristics (for example, group size, number of stock, gender, approximate age, time of entry or exit, activity, and whether a user appears to be a
day user or an overnight camper) are recorded at this time. A sample data
sheet is shown in figure 1. However, certain classes of information (such as
gender and age categories) may not be easily determined from observations.
1. Cameras.—Record necessary observations from the developed film.
Observations must be recorded in a standardized format to minimize errors
in recording. Observations include location, date, number of individuals,
number of groups, date and time of entry or exit. Observers must understand
the need to completely and correctly fill out the data form; sample observations will be useless if the data collected by the observer cannot be matched
with the appropriate registration data. Observation sheets should be filed in
a designated place. After observations are recorded, destroy negatives and
developed photos to ensure visitor privacy.
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105
2. Observers.—Observers should be stationed close enough to the registration station so that all traffic passing the station is accounted for; however,
they do not need to observe whether or not visitors actually register.
Although observers need not be beside the registration station, they should
not wander up and down the trail. Observers do not stop visitors.
Observations are recorded on a standardized form (fig. 1). Observations
include observer name, location, date, number of individuals, number of
groups, date and time of entry or exit. Observers must understand the need
to completely and correctly fill out the data form; sample observations will be
useless if the data collected by the observer cannot be matched with the
appropriate registration data. All deposited registration forms are collected
and labeled at the end of the observation period. Observation sheets and
registration cards should be filed in a designated place.
Step 11: Estimate Use
Use data are collected in accordance with the appropriate sample size and
the sampling strategy. Data obtained from registration cards are supplemented with observations obtained during the registration-rate estimation
phase. Use can be estimated for both observable and nonobservable categories of visitor, and visitor use is calculated as the number of visitors per
category, expressed as a proportion or percentage of the total number of
users.
1. Estimate Registration Rates.—Registration rate is estimated as the
ratio of the number of registered visitors (determined by the total number of
registration forms collected) to the total number of visitors (determined from
observer counts) during the sample observation periods.
Example. A total of 575 visitors registered during the 7-day registrationrate estimation phase. A random sample of n = 50 visitors indicated that 10
did not register. Therefore, the estimated registration rate r was estimated
as 40/50 = 0.8, or 80 percent. The total number of users (N) for a given period
is estimated by the total number of registered visitors (t) divided by the
registration rate:
Nˆ = t/r = 575/0.8 = 719.
The 95 percent confidence interval for the total is estimated by N ± 2·SE =
719 ± 2
[(575) ⋅ 50(50 − 40)] /(40)
2
3
= 719 ± 102, or between 617 and 821 visitors.
2. Sample Size Estimation.—Because visitor count data are collected by
counting registration cards, there may be insufficient resources available to
cover the costs and time involved in the collection, input, and processing of
large amounts of data. Sample sizes for categorical data should be specified
first. Sample sizes should be estimated for each use characteristic to be
measured, and the largest (feasible) sample size is chosen. If a stratified
sampling strategy is used, stratum sample size is calculated according to
whether proportional or disproportional representation is required.
(a) Count data. The relation used to estimate sample size is:
S
n ≅ 4 ⋅
L
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
If the sampled population is small, the finite population correction (fpc) is
used to correct for overestimation bias. Using the fpc, the estimated sample
size is:
n≅
N ⋅ S2
L2 ⋅ N
S2 +
4(2) 2
where L is the width of the interval around the projected average, and N is
the size of the true population. In this case, N is the number of days in the
season. Precision is estimated by the confidence level (generally 95 percent)
and the desired width of L. For example, the investigator may wish to be 95
percent certain that the results have a precision of ± 5 percent of the total.
Operationally feasible sample sizes are obtained by varying the amount of
precision of the estimate; highly precise estimates may require sample sizes
that are too large for practical purposes.
Example. The average number of visitors observed per day during the
compliance estimation phase was 250, with S = 160. There are 100 days in
the season (N = 100). Suppose we want to be 95 percent certain that results
will have a precision of ± 5 percent, or ± 13 visitors/day. The estimated
100(160)2
= 86. If the precision
(13 + 13)2 (100)
2
(160) +
16
is adjusted to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these
are too large or too close to the entire season of 100 days to be of practical use
due to the large underlying variance. A more reasonable level of precision
would be ± 30 percent (or ± 75 visitors per day), which would call for a sample
size of n = 15.
(b) Proportion data. Sample size (n) will be at a maximum when the
proportion of observations (p) in any given category is 0.5 (or 50 percent). The
sample size required to estimate an interval of width L around the sample
mean will be:
number of sampling days is ≈
4 ⋅ (2) ⋅ p(1 − p)
2
n=
L2
which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.
Example. Preliminary data showed that for 40 randomly selected visitors,
24 appeared to be day users. Therefore, the proportion of day users, p = 24/
40 = 0.60, and the standard error is p(1 − p) / n = (0.60)(0.40) / 40 = 0.0775.
The 95 percent confidence interval based on these data is approximately 0.6
± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size
n required for a 95 percent confidence interval with a length of at most 0.10
16(0.5)2
= 400.
(0.10)2
Therefore, it would be necessary to observe 400 visitors to obtain this amount
of precision for the estimate.
(c) Stratified sampling. If the data are stratified according to trailhead
or time block, sample sizes of each stratum must be calculated to ensure
accurate representation of the population. Sample sizes may be either
(regardless of the resulting value of p) is approximately n =
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
107
proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of
each strata or subgroup. Optimal allocation is a type of stratified sampling
where the sample size within each strata is proportional to both the size and
the variability of the sample within each stratum; the proportionality factor
[
]
is calculated as Ni ⋅ Si / ∑ ( Ni ⋅ Si ) ⋅ n. Disproportional sampling occurs when
the same size sample is drawn for each stratum (assuming equal costs to
sample each strata).
Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are
similar), whereas optimal allocation should be chosen if strata differ in the
amount of variability.
Example. In this example, data are stratified by two time blocks—weekend
days and weekdays. This stratification strategy separates out time periods
according to relative intensity of use, with the heaviest and most variable use
occurring on weekends, and relatively light and uniform use on weekdays.
For a 100-day season, there are about 72 weekdays and 28 weekend days.
Suppose the available resources (budget, labor, time) dictated that the
maximum number of days that could be sampled was n = 25. The initial value
for the standard deviation for each stratum was estimated from the data
obtained during the registration rate estimation phase. Sample sizes for each
time block are calculated as follows:
Proportional
fb
nc
Disproportional
f
n
Optimal
allocation
f
n
Stratum
sa
Weekends
(N1 = 28)
Weekdays
(N2 = 72)
88.0
0.25
7
0.43
12
0.64
16
19.2
0.25
18
0.17
12
0.36
9
aStandard
deviation.
proportion.
cSample size.
bSampling
Because the two strata differ considerably in variability, the preferred
sampling scheme is optimal allocation; with this strategy the investigator
randomly selects 16 weekend days and 9 weekdays for data collection.
3. Use Estimation.—Use characteristics estimated with this system are
limited to individual or group visit counts. Data may be expressed in terms
of: (a) the rate (for example, number of visitors per day), (b) the total (for
example, number of visitors for the season), (c) use by category (for example,
cooking method), or (d) use description (for example, length of stay).
(a) Rate of use. Suppose the number of registered visitors for a 30 day
time period was 772. A survey of 50 visitors showed that 46 had permits for
a compliance rate of 46/50 = 0.92.The estimated number of users over the 30
day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users
per day. The estimated confidence interval for the 30 day rate is:
839 ± 2 ⋅ 7722 ⋅ 50 ⋅ (50 − 46) / 463 = 839 ± 70 = (769, 909)
which converts to a confidence interval for the daily rate of (25.6, 30.3).
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(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,
corrected by the estimated bias in counts. The assumption implicit in this
method is that use remains uniform over the time period of interest; if use
patterns fluctuate considerably over the season, calibration relationships
should be updated as required, and the new relationship used to calculate use
rates for that time interval.
In this example, season length was 100 days. The overall visitor use
estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).
(c) Use by category. Frequently, visitor use is described in terms of
categories, or groups, of users; the number of users in each category is
expressed as a proportion, or percentage, of the total number of users in the
sample.
Example. On the registration form 2,975 visitors indicated their method
of cooking during their visit: stoves, wood fires, or neither. Results with a 95
percent confidence interval (using χ2 procedure based on 2 degrees of
freedom) were:
Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,
95 percent confidence interval = 0.75 ±
[
]
5.99 (0.75)(0.25) / 2, 975 = 0.75 ±
0.019 = (0.731 to 0.769);
Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,
95 percent confidence interval = 0.20 ±
[
]
5.99 (0.20)(0.80) / 2, 975 = 0.20 ±
0.018 = (0.18 to 0.22);
Neither: n3 = 149, p3 = 149/2,975 = 0.05,
95 percent confidence interval = 0.05 ± 5.99[(0.05)(0.95) / 2, 975] = 0.05 ±
0.009 = (0.04 to 0.06).
(d) Use description. One variable that may be obtained by registration
forms is length of stay. Post stratification may also be of interest.
Example. A sample of 38 registration forms had an average length of stay
of 2.4 nights with a standard error of 0.23 nights. This makes the 95 percent
confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
109
System E: Visitor Registration
System With Registration Rate
Checks and Sample Interviews
System Description ________________________________________________
This system provides information on visit counts, observable visit and
visitor characteristics, nonobservable characteristics, and summary-use
statistics. In general, visitors fill out survey cards before entering the
wilderness area, and use characteristics are obtained from the resulting
information. Supplementary information is obtained by interviewing visitors. Because registration is voluntary, the accuracy of registration data
must be determined by estimating registration rates, or compliance. Compliance rates are determined by human observers during the interview procedure. Visitor burden is low to moderate, and involves the time required by the
visitor to complete the registration form and time required for interviews.
Summary of System E:
Type of observations:
Measures of visitor use:
Data collection strategies:
Techniques/procedures:
Visitor burden:
Counts
Observable characteristics
Simple nonobservable characteristics
Complex nonobservable characteristics
Summary-use statistics
Number of individual visits
Number of group visits
Use by categories of user
Sample plan for registration station rotation (if
applicable)
• spatial
• temporal
Sample plan for registration rate estimates
Sample plan for visitor selection
Voluntary registration
Visual observations (human observers)
Interviews
Moderate
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics to Measure
Direct measures of use include individual or group visit counts. Additional
visit characteristics acquired from the registration cards include length of
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stay, entry and exit points, method of travel, group size, number of stock, and
place of residence (applicable to the party leader only). Nonobservable visit
and visitor characteristics are acquired by interviewing a random selection
of visitors. To minimize visitor burden, only simple nonobservable characteristics are recorded; these include average length of stay, average group size,
wilderness travel patterns, visitor residence, visit frequency, activities, and
visitor perception of problems, resource conditions, and so forth. Use, in
terms of number of visitors, is usually categorized by one or more nonobservable
characteristics.
Step 2: Decide on Registration Form
Standard OMB-approved registration forms are available. Alternatively,
customized registration forms can be used; however, OMB clearance must be
obtained for new forms before the study begins. According to federal legislation, OMB clearance is required if federal employees ask more than nine
members of the public the same set of questions. The proposed set of
questions, methodology, and study justification must be submitted to OMB
through the appropriate channels. For the Forest Service, application for
clearance is submitted to Information Systems in Washington, DC, which
forwards the application to the Department of Agriculture, and from there to
OMB for final approval. The time from initial submission to final OMB
clearance is usually about 3 months.
“Diary”-type registration cards can give more complete information on
wilderness experiences of visitors. Visitors complete the initial portion of the
card upon entry; this section requests basic information on the visitors or
group. The second portion requests information on the trip itself, and is filled
out by the visitor during the trip or upon leaving the wilderness area. To
reduce error, the two sections should be distinguished by separate headings
and by different colors; however, each section should have the same identification number to allow matching after collection.
Step 3: Decide on Number of Registration Stations
Registration stations are relatively inexpensive to construct, install, and
maintain. However, the number of registration stations in use at any one
time will be determined by the availability of resources (time, supplies, labor)
to ensure adequate monitoring. It is preferable to have only the number of
registration stations that can be conveniently monitored and supplied.
Stations must be kept supplied with adequate amounts of registration forms
and pencils at all times. The image of the agency suffers if visitors are
prevented from registering because supplies are lacking. The number of
stations in use will also be dictated by the number of personnel available to
conduct interviews.
Coverage of the wilderness area is performed by alternating, or rotating,
“in-use” stations across trailheads. Strategies for rotation schedules are
given in step 5.
Step 4: Develop Sampling Plan
Sampling plans must be developed for scheduling (1) rotation of registration stations (if applicable) across trailheads, and (2) observer monitoring
and interviews.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
111
1. Sample Plan for Rotating Registration Stations Across Trailheads.—
Registration stations are not expensive to construct, install, or maintain.
However, if labor or supplies are insufficient for all trailheads, registration
stations must be rotated on a systematic basis. Rotation strategies are
determined primarily by perceived differences in use occurring in either
space or time. We recommend a more-or-less permanent allocation of a
registration station to each high-use trailhead; the overall accuracy of total
use estimates will depend primarily on the accuracy of estimates obtained for
high-use areas.
(a) Spatial allocation. The following is an example of station allocation
determined by patterns in spatial use. Suppose a manager must monitor use
at four trailheads, but only two stations are available. One trailhead is
believed to account for about 60 percent of use in that wilderness area; a
second trailhead is believed to account for about 50 percent of the remaining
use. A feasible plan for station allocation would be to permanently allocate
one station to the high-use trailhead; the other station is rotated systematically across the remaining three trailheads, such that the amount of time
allocated to each trailhead is proportional to the use that trailhead is
expected to receive. That is, the second station is allocated to the second
trailhead for half of the remaining time, and allocated between the two
remaining trailheads in proportion to anticipated use.
(b) Time allocation. Stations should be placed at each trailhead for at
least two observation periods; observation periods are determined by methods of random selection (part I, chapter 3). One option is to partition the
season into 7-day weeks, then randomly select a given week or weeks as the
observation period for a given station. For example, suppose the manager
wishes to estimate use for the entire 16-week summer season; as in the above
example, there are four trailheads and two stations. One station is permanently allocated to the high-use trailhead; there are therefore three remaining trailheads to be monitored with one station. The manager decides to
partition the 16-week season into eight 2-week blocks so that the station will
be allocated to each trailhead for two separate time blocks; this leaves two
blocks as discretionary time. The order in which the station is assigned to
each trailhead is determined randomly (part I, chapter 3). Suppose the
random number sequence for the eight time blocks is 5 7 8 3 2 6 1 4, and the
random sequence for the three trailheads is 3 4 2. Then the station will be
assigned to trailhead 3 on time blocks 5 and 7, to trailhead 4 on time blocks
8 and 3, and trailhead 2 for time blocks 2 and 6.
2. Sample Plan for Interviews.—Both registration rates and nonobservable
visit characteristics are determined by contacting visitors passing a given
registration station. The procedure for estimating registration rates is
similar to the calibration procedures described for systems using mechanical
counters; visitor registration is “calibrated” by supplementary observations
so that the number of wilderness users who do not register can be accounted
for, and total visitor counts can be adjusted accordingly. Interviews are also
used to obtain information on nonobservable visit characteristics. The
number of interviews required will depend on the desired amount of precision
of both registration rate estimates and estimates of use characteristics, the
available resources, and the relative stability of visitor use over time. If use
patterns change substantially over the season, registration rates estimated
at the beginning of the season will not be applicable later in the season; the
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accuracy of registration rates must be spot checked at intervals and updated
as required.
Because human observers are used, registration rate checks may have to
be scheduled within the confines of the workweek. However, if significant
amounts of use occur outside of normal working hours, it is essential that
these time blocks are covered; volunteer labor may be one option. Observer
fatigue and boredom may be a significant problem if time blocks are
extremely long and few visitors are encountered. Sampling effort may be
apportioned according to operationally defined amounts of relative use
observed per time block. At least two observation periods should be scheduled
for each category.
Example. Past experience suggests to a wilderness ranger that the
number of visitors to a certain wilderness area is fairly constant over the
season, with approximately 20 percent of wilderness users entering wilderness area on weekdays, another 40 percent of users enter on Saturday
mornings, 10 percent on Saturday afternoons, 20 percent on Sunday mornings, and 10 percent on Sunday afternoons. A total of 10 observation periods
can be sampled with the resources available. Therefore, the ranger decides
to partition the sampling day into morning and afternoon time blocks. Time
blocks are further stratified into three operationally defined use categories:
low use, medium use, and high use. Observer effort is allocated proportional
to amount of use; thus 20 percent of sampling effort is allocated to low-use
periods (that is, two time blocks occurring on either a weekday morning or
afternoon); 40 percent effort to high-use periods (four Saturday mornings),
and the remaining effort to medium-use time periods (one Saturday afternoon, two Sunday mornings, and one Sunday afternoon. At least 4 weeks are
therefore required for this sampling plan; the specific time blocks to be
monitored are selected by random sampling procedures (part I, chapter 3).
Step 5: Construct the Registration Stations
Registration rates are greatly affected by station design. Visitors are more
likely to stop and register if the station is both attractive and functional.
Registration stations should be designed to provide (a) a place for supplies
(pencils and registration forms), (b) a convenient, solid writing surface for the
visitor to use when completing the registration form, and (c) a place to deposit
completed forms (normally a slot at the front). Registration stations may be
constructed of wood or metal, and should be set on a post at a convenient
height. Instructions must be provided which clearly detail (a) who is to
register (one person or everyone in the group), (b) when to register (upon
entry or exit), and (c) where to deposit the completed registration form.
A well-designed, easy-to-read, and attractive sign has the dual purpose of
gaining the attention of the visitor and providing relevant information.
Figure 6 illustrates an improved version of the more traditional “officiallooking” signs commonly in use. The improved sign is characterized by highquality artwork depicting different types of users (hikers and stock users,
and male and female users). The accompanying message should provide clear
instructions for the visitor, as well as a brief explanation of management’s
intended use of the information provided (for example, use estimation,
planning maintenance activities, and so forth).
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113
Figure 6—Example of an attractive
registration sign.
Step 6: Install Registration Stations
Registration rates are affected by station location. Do not establish registration stations at the trailhead or at parking areas; registration rates are
higher and vandalism is reduced if stations are located at least one-quarter
to 1 mile along the trail. However, if possible, registration stations should be
outside the wilderness boundary. The registration station should be clearly
visible from a distance; this is particularly important in stock-use areas, as
horse users need to plan ahead for a stop. The location site must have
sufficient room to allow parties leaving the area to pass a registering party,
and allow members of the group the opportunity to stop and rest while the
designated member registers.
In general, horse users register at much lower rates than hikers do; this is
partly the result of the logistic problems associated with managing pack
strings. Some experimentation with station location may be necessary to
achieve acceptable horse-user registration rates. For example, registration
stations may be located at designated or natural stock loading/unloading
areas, where stock users can register before moving the stock out on the trail.
Step 7: Select and Train the Interview Team
Careful selection and training of the personnel who are involved in
collecting data are essential if the manager or research planner is not
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performing the field research. The research planner must ensure that
interviews are conducted and observations collected in the manner required
by the study plan.
1. Personnel Selection.—Both personality and ability must be evaluated
in the selection process. The importance of visitor contact extends beyond the
quality of data obtained; it is an opportunity to present the image of the
managing agency. Select an interviewer who is friendly, reliable, knowledgeable, and trained in emergency procedures. Personnel should be familiar
with the wilderness area and be prepared to handle requests for information
about the wilderness and the surrounding area. Many of the questions from
visitors will not be related to the interview; providing information is a
courtesy which contributes to establishing rapport with the visitors and
increases visitor cooperation. Personnel should be in appropriate uniform
and possess necessary communication and safety equipment.
2. Training.—It is essential that personnel are thoroughly trained in the
data collection procedures. Training ensures that observers are already
familiar with the research directives and the interviewing process before
actual fieldwork begins. As a result, errors involved in the learning process
are reduced, and there will be greater consistency in identifying the sampling
units (in this case visitors to be interviewed) and recording responses.
Training enables observers to become familiar with various contingency
plans, to identify potential problems in the research directives, and to make
decisions if problems occur.
Preliminary, or pretest, fieldwork should be conducted before the actual
survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or
inadequacies in the procedures can be identified and eliminated, and the
consistency and accuracy of personnel can be observed and analyzed. Observers should be screened at intervals and their performance compared either
with each other or at different time points for the same observer; screening
provides a check on performance and identifies sources of error in the data.
Step 8: Collect Registration Rate and Interview Data
Information on registration rates and interview data are collected simultaneously by observers. Both types of information are collected according to
a specific plan (as described in step 4). The observer must be provided with
sufficient research material—data forms, writing tools, schedules, and so
forth—for the observation period. Observers must understand the need to
completely and correctly fill out the data forms. Observation sheets should
be filed in a designated place after the observer returns to the office.
1. Registration Rates.—Registration rate observations are obtained during the sample observation period; all traffic entering the wilderness area is
monitored, but only groups designated by the sampling plan are interviewed.
Observations must be recorded in a standardized format (see fig. 1 for a
sample form). For each data sheet, the observer should record their name, the
sampling location, the date, start time, and end time for that sample period.
The minimum information required to estimate registration rates includes
number of individuals, number of groups, method of travel, date and time of
entry or exit, and use category (day user or overnight user). All deposited
registration cards are collected at the end of the sample observation period.
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115
2. Interview Data.—The interview protocol consists of four steps: (a)
determining question format, (b) obtaining OMB clearance, (c) visitor selection, and (d) data collection.
(a) Question format. The questions asked of the visitor will be dictated
on the basis of the study objectives; that is, on the basis of what the manager
wants to know and why. Questions should be easily understood by the visitor,
they should not be too long, and there should not be too many of them. Ask
only the questions necessary to meet the study objectives, and no more. For
example, suppose the manager is interested in evaluating relative impact in
terms of time spent in different areas by various user groups. Interviews can
be limited to determining method of travel, destination, and length of stay of
visitors encountered at each trailhead; the interview will be short.
Personnel may be tempted to add additional questions “just out of curiosity”; this cannot be justified in any circumstances. Do not add questions
merely to fill up space on the interview sheet. If some inadequacy or
ambiguity becomes apparent with the set questions, questions may be added,
but only if they clarify the meaning and satisfy the requirements of step 1.
The question designer is rarely a good judge of the clarity of the questions
(Ackoff 1953); preliminary field tests are invaluable for identifying problems
before the actual field surveys begin.
(b) Obtain OMB clearance. According to federal legislation, clearance
from the Office of Management and Budget (OMB) is required if federal
employees ask more than nine members of the public the same set of
questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the
Forest Service, application for clearance is submitted to Information Systems in Washington, DC, which then forwards the application to the Department of Agriculture, and from there to OMB for final approval. The time from
initial submission to final OMB clearance is usually about 3 months.
(c) Interview selection. Visitors are selected in accordance with the
predetermined sampling plan (step 4). The location of interviews will be
determined by study objectives; visitors may be interviewed upon either
entry or exit, or both. For example, if the emphasis of the study is on the
effects of group size or place of residence on wilderness use, these factors are
unaffected by interview location. However, if the study objectives require
information on patterns of visitor use within the wilderness area (for
example, travel or camping locations, length of stay), visitors should be
interviewed as they leave.
(d) Data collection. When interviewing visitors, personnel should begin
with a standard introduction. Personnel should give their name and agency
affiliation and the reason for the interview. For example, “Hello, I am
Marilyn Holgate. I work for the Missoula District of the Lolo National Forest.
We are trying to learn more about the use of the Rattlesnake Wilderness. It
will help us with management of the area. May I ask you a few questions
about your visit today?” After the interview, thank visitors for their time.
Responses should be recorded as they are given; interviewers should not
rely on memory to fill in the interview sheet at a later time. Make sure every
item is complete and legible; data forms must include date, time, location,
and interviewer’s name. Completed data forms should be filed in a safe place.
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Step 9: Estimate Use
Use data are collected in accordance with the appropriate sample size and
the sampling strategy. Data obtained from registration cards are supplemented with observations obtained during the registration-rate estimation
phase. Use can be estimated for both observable and nonobservable categories of visitor, and visitor use is calculated as the number of visitors per
category, expressed as a proportion or percentage of the total number of users.
1. Estimate Registration Rates.—Registration rate is estimated as the
ratio of the number of registered visitors (determined by the total number of
registration forms collected) to the total number of visitors (determined from
observer counts) during the sample observation periods.
Example. A total of 575 visitors registered during the 7-day registrationrate estimation phase. A random sample of n = 50 visitors indicated that 10
did not register. Therefore, the estimated registration rate r was estimated
as 40/50 = 0.8, or 80 percent. The total number of users (N) for a given period
is estimated by the total number of registered visitors (t) divided by the
registration rate:
Nˆ = t/r = 575/0.8 = 719.
The 95 percent confidence interval for the total is estimated by N ± 2·SE =
719 ± 2
[(575) ⋅ 50(50 − 40)] /(40)
2
3
= 719 ± 102, or between 617 and 821 visitors.
2. Sample Size Estimation.—Because visitor count data are collected by
counting registration cards, there may be insufficient resources available to
cover the costs and time involved in the collection, input, and processing of
large amounts of data. Sample sizes for categorical data should be specified
first. Sample sizes should be estimated for each use characteristic to be
measured, and the largest (feasible) sample size is chosen. If a stratified
sampling strategy is used, stratum sample size is calculated according to
whether proportional or disproportional representation is required.
(a) Count data. The relation used to estimate sample size is:
S
n ≅ 4 ⋅
L
2
If the sampled population is small, the finite population correction (fpc) is
used to correct for overestimation bias. Using fpc, the estimated sample size
is:
N ⋅ S2
n≅
L2 ⋅ N
S2 +
4(2) 2
where L is the width of the interval around the projected average, and N is
the size of the true population. In this case, N is the number of days in the
season. Precision is estimated by the confidence level (generally 95 percent)
and the desired width of L. For example, the investigator may wish to be 95
percent certain that the results have a precision of ± 5 percent of the total.
Operationally feasible sample sizes are obtained by varying the amount of
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precision of the estimate; highly precise estimates may require sample sizes
that are too large for practical purposes.
Example. The average number of visitors observed per day during the
compliance estimation phase was 250, with S = 160. There are 100 days in the
season (N = 100). Suppose we want to be 95 percent certain that results will
have a precision of ± 5 percent, or ± 13 visitors/day. The estimated number of
100(160)2
= 86. If the precision is adjusted
(13 + 13)2 (100)
2
(160) +
16
to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these are too
large or too close to the entire season of 100 days to be of practical use due to
the large underlying variance. A more reasonable level of precision would be
± 30 percent (or ± 75 visitors per day), which would call for a sample size of
n = 15.
(b) Proportion data. Sample size (n) will be at a maximum when the
proportion of observations (p) in any given category is 0.5 (or 50 percent). The
sample size required to estimate an interval of width L around the sample
mean will be:
sampling days is ≈
4 ⋅ (2) ⋅ p(1 − p)
2
n=
L2
which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.
Example. Preliminary data showed that for 40 randomly selected visitors,
24 appeared to be day users. Therefore, the proportion of day users, p = 24/
40 = 0.60, and the standard error is p(1 − p) / n = (0.60)(0.40) / 40 = 0.0775.
The 95 percent confidence interval based on these data is approximately 0.6
± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size
n required for a 95 percent confidence interval with a length of at most 0.10
16(0.5)2
= 400.
(0.10)2
Therefore, it would be necessary to observe 400 visitors to obtain this amount
of precision for the estimate.
(regardless of the resulting value of p) is approximately n =
(c) Stratified sampling. If the data are stratified according to trailhead
or time block, sample sizes of each stratum must be calculated to ensure
accurate representation of the population. Sample sizes may be either
proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of
each strata or subgroup. Optimal allocation is a type of stratified sampling
where the sample size within each strata is proportional to both the size and
the variability of the sample within each stratum; the proportionality factor
[
]
is calculated as Ni ⋅ Si / ∑ ( Ni ⋅ Si ) ⋅ n. Disproportional sampling occurs
when the same size sample is drawn for each stratum (assuming equal costs
to sample each strata).
Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are
similar), whereas optimal allocation should be chosen if strata differ in the
amount of variability.
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Example. In this example, data are stratified by two time blocks—
weekend days and weekdays. This stratification strategy separates out time
periods according to relative intensity of use, with the heaviest and most
variable use occurring on weekends, and relatively light and uniform use on
weekdays. For a 100-day season, there are about 72 weekdays and 28
weekend days. Suppose the available resources (budget, labor, time) dictated
that the maximum number of days that could be sampled was n = 25. The
initial value for the standard deviation for each stratum was estimated from
the data obtained during the registration rate estimation phase. Sample
sizes for each time block are calculated as follows:
Proportional
fb
nc
Disproportional
f
n
Optimal
allocation
f
n
Stratum
sa
Weekends
(n1 = 28)
Weekdays
(n2 = 72)
88.0
0.25
7
0.43
12
0.64
16
19.2
0.25
18
0.17
12
0.36
9
aStandard
deviation.
proportion.
cSample size.
bSampling
Because the two strata differ considerably in variability, the preferred
sampling scheme is optimal allocation; with this strategy the investigator
randomly selects 16 weekend days and 9 weekdays for data collection.
3. Use Estimation.—Use characteristics estimated with this system are
limited to individual or group visit counts. Data may be expressed in terms
of: (a) the rate (for example, number of visitors per day), (b) the total (for
example, number of visitors for the season), (c) use by category (for example,
cooking method), or (d) use description (for example, length of stay).
(a) Rate of use. Suppose the number of registered visitors for a 30 day
time period was 772. A survey of 50 visitors showed that 46 had permits for
a compliance rate of 46/50 = 0.92.The estimated number of users over the 30
day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users
per day. The estimated confidence interval for the 30 day rate is
839 ± 2 ⋅ 7722 ⋅ 50 ⋅ (50 − 46) / 463 = 839 ± 70 = (769, 909)
which converts to a confidence interval for the daily rate of (25.6, 30.3).
(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,
corrected by the estimated bias in counts. The assumption implicit in this
method is that use remains uniform over the time period of interest; if use
patterns fluctuate considerably over the season, calibration relationships
should be updated as required, and the new relationship used to calculate use
rates for that time interval.
In this example, season length was 100 days. The overall visitor use
estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).
(c) Use by category. Frequently, visitor use is described in terms of
categories, or groups, of users; the number of users in each category is
expressed as a proportion, or percentage, of the total number of users in the
sample.
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119
Example. On the registration form 2,975 visitors indicated their method
of cooking during their visit: stoves, wood fires, or neither. Results with a 95
percent confidence interval (using χ2 procedure based on 2 degrees of
freedom) were:
Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,
95 percent confidence interval = 0.75 ±
[
]
5.99 (0.75)(0.25) / 2, 975 = 0.75 ±
0.019 = (0.731 to 0.769);
Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,
95 percent confidence interval = 0.20 ±
[
]
[
]
5.99 (0.20)(0.80) / 2, 975 = 0.20 ±
0.018 = (0.18 to 0.22);
Neither: n3 = 149, p3 = 149/2,975 = 0.05,
95 percent confidence interval = 0.05 ±
5.99 (0.05)(0.95) / 2, 975 = 0.05 ±
0.009 = (0.04 to 0.06).
(d) Use description. One variable that may be obtained by registration
forms is length of stay. Post stratification may also be of interest.
Example. A sample of 38 registration forms had an average length of stay
of 2.4 nights with a standard error of 0.23 nights. This makes the 95 percent
confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).
Hiking is by far the most common method of wilderness travel.
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System F: Permit System With
Compliance Checks
System Description ________________________________________________
Permits are mandatory use-authorization forms issued by the agency. The
information obtained is constrained by what is required by the permit form;
this system provides sufficient information to estimate basic visit counts,
visit and visitor characteristic data, and may enable estimates of certain
summary-use statistics. Compliance checks are required for accurate estimation of total use. Because visitors are responsible for obtaining permits,
visitor burden is relatively high.
Summary of System F:
Type of observations:
Measures of visitor use:
Data collection strategies:
Techniques/procedures:
Visitor burden:
Counts
Observable characteristics
Simple nonobservable characteristics
Complex nonobservable characteristics
Number of individual visits
Number of group visits
Total number of users
Use by category of user
Summary-use statistics
Permit-issue method
Visitor selection sampling for compliance checks
Permits
Compliance checks
Moderate to high
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics
Use characteristics that can be obtained are restricted by the permit
format. Information obtained from permits can include the number of
individuals or groups, group size, method of travel, anticipated dates of entry
and exit, length of stay, and place of residence. If mailback sections are
included with the permit, the permit holder can document various triprelated observations, such as number of encounters, travel routes and
destinations, actual length of stay, and perceptions of wilderness conditions.
Step 2: Decide on a Permit Form
Standard OMB-approved permits are available for each agency. Alternatively, customized permit formats can be used. However, OMB clearance
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
121
must be obtained before the study begins if permits are to be issued in a
revised format; this includes the addition of questions to standard permit
forms. According to federal legislation, OMB clearance is required if federal
employees ask more than nine members of the public the same set of
questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the
Forest Service, application for clearance is submitted to Information Systems in Washington, DC, which forwards the application to the Department
of Agriculture, and from there to OMB for final approval. The time from
initial submission to final OMB clearance is usually about 3 months.
Clearance is not required if shortened versions of the standard permit with
fewer questions are used.
Step 3: Establish a Permit-Issue Procedure
The procedure for issuing permits will be determined by (1) the reason for
issuing permits, and (2) the source of issue.
1. Reasons for Permit Issue.—Permits are issued to (a) provide a means of
public contact, (b) restrict use or categories of user, and (c) monitor use.
(a) Public contact. If the objective in issuing permits is to create
opportunities for public contact opportunity, visitors will be required to
obtain permits in person at a centralized agency facility, such as a visitor
center or ranger station. Visitor contact with a trained agency representative
is valuable for promoting the professional image of the agency and increasing
visitor knowledge of regulations, appropriate low-impact behaviors, potential hazards, and wilderness conditions. Visitors have the opportunity to
discuss possible routes and destinations within the wilderness area, and to
obtain other information of interest to them.
(b) Use restriction. If the objective in issuing permits is to restrict use,
visitors will be required to obtain permits at a centralized agency facility,
such as a visitor center or ranger station. Alternatively, if adequate computer
facilities are available, permits can be issued from a number of different field
offices by means of a computerized reservation system so that the number of
permits available at any time can be tracked.
(c) Use monitoring. If permits are issued with the objective of collecting
accurate visitor use data, there are no associated restrictions on where or
how permits are issued. Permits may be issued by the agency or self-issued;
numbers may be limited or unlimited.
2. Source of Permit Issue.—Permits are usually issued by agency personnel, but may be self-issued, or distributed through a cooperative arrangement with local vendors.
In the majority of cases, permits are issued from a central location by the
managing agency. Staff at local ranger stations, information centers, or
National Forest offices are responsible for issuing permits. Occasionally,
permits may be reserved; reservations may be made by telephone or mail, or
in other cases must be made in person if “no-shows” are a problem. Reserved
permits may be mailed, or held until picked up by the visitor.
Self-issued permits are usually obtained from some convenient location. If
permits are unlimited, they may be obtained from a station located outside
the agency office or at trailheads, or from alternative locations, such as local
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businesses. However, if permit numbers are limited, they must be obtained
from a central location.
If there are restrictions on certain types of users, permit-issue locations
may be placed so as to accommodate different user groups. For example, if
overnight use of a wilderness area must be rationed but day use is essentially
unrestricted, a limited number of overnight permits are made available at
some central location, whereas self-issued day-use permits are located at
trailheads.
Permits may be issued through cooperative arrangements with local
vendors or businesses. Wilderness permits may be issued by convenience
stores, bait shops, commercial outfitters, travel information centers, or
nearby campgrounds.
Step 4: Decide on Method of Implementing Compliance Checks
Unlike registration systems, which are voluntary, permit systems are
mandatory. Visitors must obtain a permit to enter the wilderness area;
otherwise they are not in compliance with regulations. However, accuracy of
use estimation will be compromised if rates of compliance are unknown.
Permit compliance may be as low as 53 percent with self-issued day-use
permits to as high as 90 percent; compliance varies with type of user group,
and increases with increased levels of enforcement, increased publicity about
permit requirements, and increased visitor awareness of permit requirements.
The procedure for estimating compliance is similar to the calibration
procedures described for systems using mechanical counters. Visitor counts
obtained from a tally of permits are “calibrated” by supplementary observations so that the number of wilderness users who do not obtain permits can
be accounted for, and total visitor counts can be adjusted accordingly.
Interviews are also used to obtain information on nonobservable visit
characteristics. The number of interviews required will depend on the
desired amount of precision of both compliance estimates and estimates of
use characteristics, the available resources, and the relative stability of
visitor use over time. If use patterns change substantially over the season,
compliance rates estimated at the beginning of the season will not be
applicable later in the season; the accuracy of compliance rates must be spot
checked at intervals and updated as required.
Frequently, permit compliance is determined in the course of routine
wilderness ranger patrol. Rangers check for permit compliance as visitor
groups are encountered, and tally the proportion of those encountered who
do not have a permit; this is the so-called “roaming observation” technique.
However, this type of visitor sampling results in extremely biased estimates
of visitor use. Bias occurs because the probability of visitor contact depends
on when and where the observer travels. Scheduling is not random but
deliberately selected to coincide with periods of heaviest use; the probability
that a visitor group will be encountered is proportional to the length of time
spent in a given area, observer location in relation to visitor distance
traveled, and so on.
Unbiased data can be obtained only by implementing statistical sampling
strategies. Permit checkpoints should be established, and visitors sampled
according to a predetermined sampling plan. Sampling may be strictly random,
or stratified by day and systematic within that day. Sample sizes are determined with reference to the population of interest, the expected variation of
the response variables, and the specified sampling plan (part I, chapter 3).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
123
Step 5: Purchase Equipment
If permits are self-issued, permit stations need to be constructed. These
stations should be both attractive and functional. Self-issue permit stations
should be designed to provide (1) a place for supplies (pencils and permit
forms), (2) a convenient, solid writing surface for the visitor to use when
completing the permit, and (3) a place to deposit completed agency copy
(normally a slot at the front). Stations may be constructed of wood or metal,
and should be set on a post at a convenient height. An attractive and easyto-read sign should be posted with instructions detailing (1) why a permit is
required, (2) who is to obtain a permit (one person or everyone in the group),
(3) where to deposit the completed agency copy, and (4) the consequences of
being found in violation.
Step 6: Estimate Use
Use data are collected in accordance with the appropriate sample size and
the sampling strategy. Data obtained from permits are supplemented with
observations obtained during the permit compliance rate estimation phase.
Use can be estimated for both observable and nonobservable categories of
visitor, and visitor use is calculated as the number of visitors per category,
expressed as a proportion or percentage of the total number of users.
1. Estimate Permit Compliance Rates.—Permit compliance rate is estimated as the ratio of the number of permit holders (determined by the total
number of permits collected) to the total number of visitors (determined from
observer counts) during the sample observation periods.
Example. A total of 575 visitors obtained permits during the 7-day permit
compliance rate estimation phase. A random sample of n = 50 visitors
indicated that 10 did not obtain permits. Therefore, the estimated permit
compliance rate r was estimated as 40/50 = 0.8, or 80 percent. The total
number of users (N) for a given period is estimated by the total number of
permit holding visitors (t) divided by the permit compliance rate:
Nˆ = t/r = 575/0.8 = 719
The 95 percent confidence interval for the total is estimated by N ± 2· SE =
719 ± 2
[(575) ⋅ 50(50 − 40)] /(40)
2
3
= 719 ± 102, or between 617 and 821 visitors.
2. Sample Size Estimation.—Because visitor count data are collected by
counting permits, there may be insufficient resources available to cover the
costs and time involved in the collection, input, and processing of large
amounts of data. Sample sizes for categorical data should be specified first.
Sample sizes should be estimated for each use characteristic to be measured,
and the largest (feasible) sample size is chosen. If a stratified sampling
strategy is used, stratum sample size is calculated according to whether
proportional or disproportional representation is required.
(a) Count data. The relation used to estimate sample size is:
S
n ≅ 4 ⋅
L
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If the sampled population is small, the finite population correction (fpc) is
used to correct for overestimation bias. Using the fpc, the estimated sample
size is:
n≅
N ⋅ S2
L2 ⋅ N
S2 +
4(2)2
where L is the width of the interval around the projected average, and N is
the size of the true population. In this case, N is the number of days in the
season. Precision is estimated by the confidence level (generally 95 percent)
and the desired width of L. For example, the investigator may wish to be 95
percent certain that the results have a precision of ± 5 percent of the total.
Operationally feasible sample sizes are obtained by varying the amount of
precision of the estimate; highly precise estimates may require sample sizes
that are too large for practical purposes.
Example. The average number of visitors observed per day during the
compliance estimation phase was 250, with S = 160. There are 100 days in
the season (N = 100). Suppose we want to be 95 percent certain that results
will have a precision of ± 5 percent, or ± 13 visitors/day. The estimated
100(160)2
= 86. If the precision
2
13 + 13) (100)
(
2
(160) +
16
is adjusted to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these
are too large or too close to the entire season of 100 days to be of practical use
due to the large underlying variance. A more reasonable level of precision
would be ± 30 percent (or ± 75 visitors per day), which would call for a sample
size of n = 15.
(b) Proportion data. Sample size (n) will be at a maximum when the
proportion of observations (p) in any given category is 0.5 (or 50 percent). The
sample size required to estimate an interval of width L around the sample
mean will be:
number of sampling days is ≈
4 ⋅ (2) ⋅ p(1 − p)
2
n=
L2
which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.
Example. Preliminary data showed that for 40 randomly selected visitors,
24 appeared to be day users. Therefore, the proportion of day users, p = 24/
40 = 0.60, and the standard error is p(1 − p) / n = (0.60)(0.40) / 40 = 0.0775.
The 95 percent confidence interval based on these data is approximately 0.6
± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size
n required for a 95 percent confidence interval with a length of at most 0.10
16(0.5)2
= 400.
(0.10)2
Therefore, it would be necessary to observe 400 visitors to obtain this amount
of precision for the estimate.
(c) Stratified sampling. If the data are stratified according to trailhead
or time block, sample sizes of each stratum must be calculated to ensure
accurate representation of the population. Sample sizes may be either
(regardless of the resulting value of p) is approximately n =
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125
proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of
each strata or subgroup. Optimal allocation is a type of stratified sampling
where the sample size within each strata is proportional to both the size and
the variability of the sample within each stratum; the proportionality factor
[
is calculated as Ni ⋅ Si /
∑ ( N ⋅ S )] ⋅ n. Disproportional sampling occurs when
i
i
the same size sample is drawn for each stratum (assuming equal costs to
sample each strata).
Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are
similar), whereas optimal allocation should be chosen if strata differ in the
amount of variability.
Example. In this example, data are stratified by two time blocks—
weekend days and weekdays. This stratification strategy separates out time
periods according to relative intensity of use, with the heaviest and most
variable use occurring on weekends, and relatively light and uniform use on
weekdays. For a 100-day season, there are about 72 weekdays and 28
weekend days. Suppose the available resources (budget, labor, time) dictated
that the maximum number of days that could be sampled was n = 25. The
initial value for the standard deviation for each stratum was estimated from
the data obtained during the permit compliance rate estimation phase.
Sample sizes for each time block are calculated as follows:
Proportional
fb
nc
Disproportional
f
n
Optimal
allocation
f
n
Stratum
sa
Weekends
(n1 = 28)
Weekdays
(n2 = 72)
88.0
0.25
7
0.43
12
0.64
16
19.2
0.25
18
0.17
12
0.36
9
aStandard
deviation.
proportion.
cSample size.
bSampling
Because the two strata differ considerably in variability, the preferred
sampling scheme is optimal allocation; with this strategy the investigator
randomly selects 16 weekend days and 9 weekdays for data collection.
3. Use Estimation.—Use characteristics estimated with this system are
limited to individual or group visit counts. Data may be expressed in terms
of: (a) the rate (for example, number of visitors per day), (b) the total (for
example, number of visitors for the season), (c) use by category (for example,
cooking method), or (d) use description (for example, length of stay).
(a) Rate of use. Suppose the number of visitors with permits for a 30 day
time period was 772. A survey of 50 visitors showed that 46 had permits for
a compliance rate of 46/50 = 0.92. The estimated number of users over the 30
day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users
per day. The estimated confidence interval for the 30 day rate is 839 ±
2 ⋅ 7722 ⋅ 50 ⋅ (50 − 46) / 463 = 839 ± 70 = (769, 909), which converts to a confi-
dence interval for the daily rate of (25.6, 30.3).
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(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,
corrected by the estimated bias in counts. The assumption implicit in this
method is that use remains uniform over the time period of interest; if use
patterns fluctuate considerably over the season, calibration relationships
should be updated as required, and the new relationship used to calculate use
rates for that time interval.
In this example, season length was 100 days. The overall visitor use
estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).
(c) Use by category. Frequently, visitor use is described in terms of
categories, or groups, of users; the number of users in each category is
expressed as a proportion, or percentage, of the total number of users in the
sample.
Example. On the permit form 2,975 visitors indicated their method of
cooking during their visit: stoves, wood fires, or neither. Results with a 95
percent confidence interval (using χ2 procedure based on 2 degrees of
freedom) were:
Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,
95 percent confidence interval = 0.75 ± 5.99[(0.75)(0.25) / 2, 975] = 0.75 ± 0.019
= (0.731 to 0.769);
Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,
95 percent confidence interval = 0.20 ± 5.99[(0.20)(0.80) / 2, 975] = 0.20 ± 0.018
= (0.18 to 0.22);
Neither: n3 = 149, p3 = 149/2,975 = 0.05,
95 percent confidence interval = 0.05 ± 5.99[(0.05)(0.95) / 2, 975] = 0.05 ± 0.009
= (0.04 to 0.06).
(d) Use description. One variable that may be obtained by permits is
length of stay. Post stratification may also be of interest.
Example. A sample of 38 permits had an average length of stay of 2.4
nights with a standard error of 0.23 nights. This makes the 95 percent
confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).
Day-use horseback rider registration ranges from a low of
0 percent to 89 percent.
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127
System G: Permit System With
Compliance Checks and Sample
Interviews
System Description ________________________________________________
Permits are mandatory use-authorization forms issued by the agency. Use
information obtained is determined by the permit form and by the interview
format; this system provides sufficient information to estimate summaryuse statistics, as well as basic visit counts, visit and visitor characteristic
data. Compliance checks are required for accurate estimation of total use. A
random selection of visitors is interviewed to obtain supplementary information not provided by the permit. Because visitors are responsible for obtaining permits, and because visitors are contacted directly for interviews, visitor
burden is relatively high.
Summary of System G:
Type of observations:
Measures of visitor use:
Data collection strategies:
Techniques/procedures:
Visitor burden:
Counts
Observable characteristics
Simple nonobservable characteristics
Complex nonobservable characteristics
Number of individual visits
Number of group visits
Use by categories of user
Summary-use statistics
Permit-issue process
Sampling plan for visitor selection
Permits
Compliance checks
Sample interviews
Moderate to high
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics
Use characteristics that can be obtained are limited only by the permit
format. Information obtained from permits can include the number of
individuals or groups, group size, method of travel, anticipated dates of entry
and exit, length of stay, and place of residence. Mailback sections attached
to the permit enable the permit holder to document various trip-related
observations, such as number of encounters, travel routes and destinations,
actual length of stay, and perceptions of wilderness conditions.
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Nonobservable visit and visitor characteristics not on the permit form are
acquired by interviewing a random selection of visitors. The characteristics
include specific length-of-stay information, anticipated wilderness travel
patterns and routes, visit frequency, activities, and visitor perception of
problems and resource conditions, past wilderness experience, knowledge of
regulations and low-impact procedures, preferences for various management strategies, and so forth.
Step 2: Decide on a Permit Form
Standard OMB-approved permits are available for each agency. Alternatively, customized permit formats can be used. However, OMB clearance
must be obtained before the study begins if permits are to be issued in a
revised format; this includes the addition of questions to standard permit
forms. According to federal legislation, OMB clearance is required if federal
employees ask more than nine members of the public the same set of
questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the
Forest Service, application for clearance is submitted to that Agency’s
Information Systems office in Washington, DC, which forwards the application to the Department of Agriculture, and from there to OMB for final
approval. The time from initial submission to final OMB clearance is usually
about 3 months. Clearance is not required if shortened versions of the
standard permit with fewer questions are used.
Step 3: Establish a Permit-Issue Procedure
The procedure for issuing permits will be determined by (1) the reason for
issuing permits, and (2) the source of issue.
1. Reasons for Permit Issue.—Permits are issued to (a) provide a means
of public contact, (b) restrict use or categories of user, and (c) monitor use.
(a) Public contact. If the objective in issuing permits is to create
opportunities for public contact opportunity, visitors will be required to
obtain permits in person at a centralized agency facility, such as a visitor
center or ranger station. Visitor contact with a trained agency representative is valuable for promoting the professional image of the agency and
increasing visitor knowledge of regulations, appropriate low-impact behaviors, potential hazards, and wilderness conditions. Visitors have the opportunity to discuss possible routes and destinations within the wilderness
area, and to obtain other information of interest to them.
(b) Use restriction. If the objective in issuing permits is to restrict use,
visitors will be required to obtain permits at a centralized agency facility,
such as a visitor center or ranger station. Alternatively, if adequate computer facilities are available, permits can be issued from a number of
different field offices by means of a computerized reservation system so that
the number of permits available at any time can be tracked.
(c) Use monitoring. If permits are issued with the objective of collecting
accurate visitor use data, there are no associated restrictions on where or
how permits are issued. Permits may be issued by the agency or self-issued;
numbers may be limited or unlimited.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
129
2. Source of Permit Issue.—Permits are usually issued by agency personnel, but may be self-issued, or distributed through a cooperative arrangement with local vendors.
In the majority of cases, permits are issued from a central location by the
managing agency. Staff at local ranger stations, information centers, or
National Forest offices are responsible for issuing permits. Occasionally,
permits may be reserved; reservations may be made by telephone or mail, or
in other cases must be made in person if “no-shows” are a problem. Reserved
permits may be mailed, or held until picked up by the visitor.
Self-issued permits are usually obtained from some convenient location. If
wilderness use is unrestricted, permit access does not need to be monitored
closely. As a result, permits may be obtained from a station located outside
the agency office or at trailheads, or from alternative locations, such as local
businesses. However, if permit numbers are limited, permits must be
obtained from a central location where permit acquisition can be regulated.
If there are restrictions on certain types of users, permit-issue locations
may be placed so as to accommodate different user groups. For example, if
overnight use of a wilderness area must be rationed but day use is essentially
unrestricted, a limited number of overnight permits are made available at
some central location, whereas self-issued day-use permits are located at
trailheads.
Permits may be issued through cooperative arrangements with local
vendors or businesses. Wilderness permits may be issued by convenience
stores, bait shops, commercial outfitters, travel information centers, or
nearby campgrounds.
Step 4: Develop Sampling Plan
Sample plans must be developed for:
1. Implementing compliance checks, and
2. Selecting visitors for interviews.
1. Compliance Checks.—Unlike registration systems, which are voluntary, permit systems are mandatory. Visitors must obtain a permit to enter
the wilderness area, otherwise they are not in compliance with regulations.
However, accuracy of use estimation will be compromised if rates of compliance are unknown. Permit compliance may be as low as 53 percent with selfissued day-use permits, to as high as 90 percent; compliance varies with type
of user group, and increases with increased levels of enforcement, increased
publicity about permit requirements, and increased visitor awareness of
permit requirements.
The procedure for estimating compliance is similar to the calibration
procedures described for systems using mechanical counters. Visitor counts
obtained from a tally of permits are “calibrated” by supplementary observations so that the number of wilderness users who do not obtain permits can
be accounted for, and total visitor counts can be adjusted accordingly. The
number of compliance checks required will depend on the desired amount of
precision, the available resources, and the relative stability of visitor use over
time. If use patterns change substantially over the season, compliance rates
estimated at the beginning of the season will not be applicable later in the
season; the accuracy of compliance rates must be spot checked at intervals
and updated as required.
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Frequently, permit compliance is determined in the course of routine
wilderness ranger patrol. Rangers check for permit compliance as visitor
groups are encountered, and tally the proportion of those encountered who
do not have a permit; this is the so-called “roaming observation” technique.
However, this type of visitor sampling results in extremely biased estimates
of visitor use. Bias occurs because the probability of visitor contact depends
on when and where the observer travels. Scheduling is not random but
deliberately selected to coincide with periods of heaviest use; the probability
that a visitor group will be encountered is proportional to the length of time
spent in a given area, and observer location in relation to visitor distance
traveled.
Unbiased data can be obtained only by implementing statistical sampling
strategies. Permit checkpoints should be established, and visitors sampled
according to a predetermined sampling plan. Sampling may be strictly
random, or stratified by day and systematic within that day. Sample sizes are
determined with reference to the population of interest, the expected variation of the response variables, and the specified sampling plan (part I,
chapter 3).
2. Interviews.—Interviews are conducted by contacting visitors at a checkpoint station outside the wilderness boundary. Interviews are used to obtain
information on non-observable visit characteristics.
The two steps in the formulation of an appropriate sampling plan for visitor
selection are an estimate of the sample size, and a time schedule.
(a) Sample size estimation. Determination of the appropriate sample
size requires a preliminary estimate of the variability in the observations.
Preliminary estimates are obtained from a pilot study, or from data collected
in previous years. A common requirement of many wilderness studies is the
comparison of count or frequency data by category; categories are identified
by specific visit characteristic. To ensure adequate representation, sampling
may have to be stratified by category. See part I, chapter 3, for further details
of sample design.
(b) Time schedule. For the sample to be representative of all visitors
entering the wilderness area, interviews must be scheduled according to a
statistical sampling plan. Unless the wilderness area has a strictly enforced
permit program, visitors cannot be randomly selected for interviewing prior
to arrival. If there is no regulation of visitor entry and exit, the alternative
is the random selection of interview days, followed by random selection of
visitors within the sample day. Sampling may be completely random,
systematic (for example, selective censusing of every tenth wilderness
visitor, or every fifth car passing a checkpoint), stratified, or a combination
of these (part I, chapter 3).
Step 5: Purchase Equipment
If permits are self-issued, permit stations need to be constructed. These
stations should be both attractive and functional. Self-issue permit stations
should be designed to provide (a) a place for supplies (pencils and permit
forms, (b) a convenient, solid writing surface for the visitor to use when
completing the permit, and (c) a place to deposit completed agency copy
(normally a slot at the front). Stations may be constructed of wood or metal,
and should be set on a post at a convenient height. An attractive and easyto-read sign should be posted with instructions detailing (a) why a permit is
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
131
required, (b) who is to obtain a permit (one person or everyone in the group),
(c) where to deposit the completed agency copy, and (d) the consequences of
being found in violation.
Step 6: Select and Train the Interview Team
Careful selection and training of the personnel who are involved in
collecting data are essential if the manager or research planner is not
performing the field research. The research planner must ensure that
interviews are conducted and observations collected in the manner required
by the study plan.
1. Personnel Selection.—Both personality and ability must be evaluated
in the selection process. The importance of visitor contact extends beyond the
quality of data obtained; it is an opportunity to present the image of the
managing agency. Select an interviewer who is friendly, reliable, knowledgeable, and trained in emergency procedures. Personnel should be familiar
with the wilderness area and be prepared to handle requests for information
about the wilderness and the surrounding area. Many of the questions from
visitors will not be related to the interview; providing information is a
courtesy which contributes to establishing rapport with the visitors and
increases visitor cooperation. Personnel should be in appropriate uniform
and possess necessary communication and safety equipment.
2. Training.—It is essential that personnel are thoroughly trained in the
data collection procedures. Training ensures that observers are already
familiar with the research directives and the interviewing process before
actual fieldwork begins. As a result, errors involved in the learning process
are reduced, and there will be greater consistency in identifying the sampling
units (in this case visitors to be interviewed) and recording responses.
Training enables observers to become familiar with various contingency
plans, to identify potential problems in the research directives, and to make
decisions if problems occur.
Preliminary, or pretest, fieldwork should be conducted before the actual
survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or
inadequacies in the procedures can be identified and eliminated, and the
consistency and accuracy of personnel can be observed and analyzed. Observers should be screened at intervals, and their performance compared either
with each other or at different time points for the same observer; screening
provides a check on performance and identifies sources of error in the data.
Step 7: Collect Compliance Rate and Interview Data
Information on compliance rates and interview data are collected separately by observers. Both types of information are collected according to a
specific plan (as described in step 4). The observer must be provided with
sufficient research material—data forms, writing tools, schedules, and so
forth,—for the observation period. Observers must understand the need to
completely and correctly fill out the data forms. Observation sheets should
be filed in a designated place after the observer returns to the office.
1. Compliance Rates.—Compliance rate observations are obtained during
the sample observation period (step 4). Observations must be recorded in a
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standardized format (see fig. 1 for a sample form). For each data sheet, the
observer should record their name, the sampling location, the date, start
time, and end time for that sample period. The minimum information
required to estimate compliance rates includes number of individuals,
number of groups, method of travel, date and time of entry or exit, and use
category (day user or overnight user).
2. Interview Data.—The interview protocol consists of four steps: (a) determining question format, (b) obtaining OMB clearance, (c) visitor selection,
and (d) data collection.
(a) Question format. The questions asked of the visitor will be dictated
by the study objectives; that is, on the basis of what the manager wants to
know and why. Questions should be easily understood by the visitor, they
should not be too long, and there should not be too many of them. The major
principle in question development is the necessity to keep visitor burden to a
minimum. Ask only the questions necessary to meet the study objectives, and
no more.
The questions asked of the respondents will depend on what kind of
information is required to meet the study objectives. Questions can be
categorized on the basis of one or more of the following types of information:
• Attitudes: what people say they want or how they feel about something;
• Beliefs: what people think is true or false;
• Behavior: what people do;
• Attributes: what people are (personal or demographic features).
Questions must be clearly identified according to information type, otherwise responses will lead to a different type of information than required by
the study objectives.
The question designer is rarely a good judge of the clarity of the questions
(Ackoff 1953). Preliminary field tests are invaluable for identifying problems,
and should be conducted before the actual field surveys begin. Colleagues,
potential “users” of the data, and, if possible, a small pretest sample of
prospective respondents should fill out the questionnaire; a debriefing
session should follow to identify problems. If some inadequacy or ambiguity
becomes apparent with the set questions, questions may be added, but only
if they clarify the meaning and satisfy the requirements of step 1.
(b) Obtain OMB clearance. According to federal legislation, clearance
from the Office of Management and Budget (OMB) is required if federal
employees ask more than nine members of the public the same set of
questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the
Forest Service, application for clearance is submitted to Information Systems in Washington, DC, which then forwards the application to the Department of Agriculture, and from there to OMB for final approval. The time from
initial submission to final OMB clearance is usually about 3 months.
(c) Visitor selection. Visitors are selected in accordance with the predetermined sampling plan (step 4). The location of interviews will be determined by study objectives; visitors may be interviewed upon either entry or
exit, or both. For example, if the emphasis of the study is on the effects of
group size or place of residence on wilderness use, these factors are unaffected by interview location. However, if the study objectives require information on patterns of visitor use within the wilderness area (for example,
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
133
travel or camping locations, length of stay), visitors should be interviewed as
they leave. Visitors should not be interviewed inside the wilderness boundary (to avoid threats to the visitor experience from management presence).
(d) Data collection. When interviewing visitors, personnel should begin
with a standard introduction. Personnel should give their name and agency
affiliation and the reason for the interview. For example, “Hello, I am
Marilyn Holgate. I work for the Missoula District of the Lolo National Forest.
We are trying to learn more about the use of the Rattlesnake Wilderness. It
will help us with management of the area. May I ask you a few questions
about your visit today?” After the interview, thank visitors for their time.
Personnel may be tempted to add additional questions “just out of curiosity”;
this cannot be justified in any circumstances.
Responses should be recorded as they are given; interviewers should not
rely on memory to fill in the interview sheet at a later time. Make sure every
item is complete and legible; data forms must include date, time, location,
and interviewer’s name. Completed data forms should be filed in a safe place.
Step 8: Estimate Use
Use data are collected in accordance with the appropriate sample size and
the sampling strategy. Data obtained from permits are supplemented with
observations obtained during the permit compliance rate estimation phase.
Use can be estimated for both observable and nonobservable categories of
visitor, and visitor use is calculated as the number of visitors per category,
expressed as a proportion or percentage of the total number of users.
1. Estimate Permit Compliance Rates.—Permit compliance rate is estimated as the ratio of the number of permit holders (determined by the total
number of permits collected) to the total number of visitors (determined from
observer counts) during the sample observation periods.
Example. A total of 575 visitors obtained permits during the 7-day permit
compliance rate estimation phase. A random sample of n = 50 visitors
indicated that 10 did not obtain permits. Therefore, the estimated permit
compliance rate r was estimated as 40/50 = 0.8, or 80 percent. The total
number of users (N) for a given period is estimated by the total number of
permit holding visitors (t) divided by the permit compliance rate:
Nˆ = t/r = 575/0.8 = 719.
The 95 percent confidence interval for the total is estimated by N ± 2·SE =
719 ± 2
[(575) ⋅ 50(50 − 40)] /(40)
2
3
= 719 ± 102, or between 617 and 821 visitors.
2. Sample Size Estimation.—Because visitor count data are collected by
counting permits, there may be insufficient resources available to cover the
costs and time involved in the collection, input, and processing of large
amounts of data. Sample sizes for categorical data should be specified first.
Sample sizes should be estimated for each use characteristic to be measured,
and the largest (feasible) sample size is chosen. If a stratified sampling
strategy is used, stratum sample size is calculated according to whether
proportional or disproportional representation is required.
(a) Count data. The relation used to estimate sample size is:
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
S
n ≅ 4 ⋅
L
2
If the sampled population is small, the finite population correction (fpc) is used
to correct for overestimation bias. Using fpc, the estimated sample size is:
n≅
N ⋅ S2
L2 ⋅ N
S2 +
4(2) 2
where L is the width of the interval around the projected average, and N is
the size of the true population. In this case, N is the number of days in the
season. Precision is estimated by the confidence level (generally 95 percent)
and the desired width of L. For example, the investigator may wish to be 95
percent certain that the results have a precision of ± 5 percent of the total.
Operationally feasible sample sizes are obtained by varying the amount of
precision of the estimate; highly precise estimates may require sample sizes
that are too large for practical purposes.
Example. The average number of visitors observed per day during the
compliance estimation phase was 250, with S = 160. There are 100 days in
the season (N = 100). Suppose we want to be 95 percent certain that results
will have a precision of ± 5 percent, or ± 13 visitors/day. The estimated
100(160)2
If the precision
(13 + 13)2 (100) = 86.
2
(160) +
16
is adjusted to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these
are too large or too close to the entire season of 100 days to be of practical use
due to the large underlying variance. A more reasonable level of precision
would be ± 30 percent (or ± 75 visitors per day), which would call for a sample
size of n = 15.
(b) Proportion data. Sample size (n) will be at a maximum when the
proportion of observations (p) in any given category is 0.5 (or 50 percent). The
sample size required to estimate an interval of width L around the sample
mean will be:
number of sampling days is ≈
4 ⋅ (2) ⋅ p(1 − p)
2
n=
L2
which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.
Example. Preliminary data showed that for 40 randomly selected visitors,
24 appeared to be day users. Therefore, the proportion of day users, (p) = 24/
40 = 0.60, and the standard error is
p(1 − p) / n =
(0.60)(0.40) / 40 = 0.0775.
The 95 percent confidence interval based on these data is approximately 0.6
± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size
n required for a 95 percent confidence interval with a length of at most 0.10
16(0.5)2
= 400.
(0.10)2
Therefore, it would be necessary to observe 400 visitors to obtain this amount
of precision for the estimate.
(regardless of the resulting value of p) is approximately n =
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135
(c) Stratified sampling. If the data are stratified according to trailhead
or time block, sample sizes of each stratum must be calculated to ensure
accurate representation of the population. Sample sizes may be either
proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of
each strata or subgroup. Optimal allocation is a type of stratified sampling
where the sample size within each strata is proportional to both the size and
the variability of the sample within each stratum; the proportionality factor
[
]
is calculated as Ni ⋅ Si / ∑ ( Ni ⋅ Si ) ⋅ n. Disproportional sampling occurs when
the same size sample is drawn for each stratum (assuming equal costs to
sample each strata).
Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are
similar), whereas optimal allocation should be chosen if strata differ in the
amount of variability.
Example. In this example, data are stratified by two time blocks—weekend
days and weekdays. This stratification strategy separates out time periods
according to relative intensity of use, with the heaviest and most variable use
occurring on weekends, and relatively light and uniform use on weekdays.
For a 100-day season, there are about 72 weekdays and 28 weekend days.
Suppose the available resources (budget, labor, time) dictated that the
maximum number of days that could be sampled was n = 25. The initial value
for the standard deviation for each stratum was estimated from the data
obtained during the permit compliance rate estimation phase. Sample sizes
for each time block are calculated as follows:
Proportional
fb
nc
Disproportional
f
n
Optimal
allocation
f
n
Stratum
sa
Weekends
(n1 = 28)
Weekdays
(n2 = 72)
88.0
0.25
7
0.43
12
0.64
16
19.2
0.25
18
0.17
12
0.36
9
aStandard
deviation.
proportion.
cSample size.
bSampling
Because the two strata differ considerably in variability, the preferred
sampling scheme is optimal allocation; with this strategy the investigator
randomly selects 16 weekend days and 9 weekdays for data collection.
3. Use Estimation.—Use characteristics estimated with this system include individual or group visit counts. Data may be expressed in terms of:
(a) the rate (for example, number of visitors per day), (b) the total (for example,
number of visitors for the season), (c) use by category (for example, cooking
method), (d) use description (for example, length of stay), or (e) summary-use
statistics (for example, recreation visitor days).
(a) Rate of use. Suppose the number of visitors with permits for a 30 day
time period was 772. A survey of 50 visitors showed that 46 had permits for
a compliance rate of 46/50 =0.92.The estimated number of users over the
30 day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28
users per day. The estimated confidence interval for the 30 day rate is
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839 ± 2 ⋅ 7722 ⋅ 50 ⋅ (50 − 46) / 463 = 839 ± 70 = (769, 909), which converts to a
confidence interval for the daily rate of (25.6, 30.3).
(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,
corrected by the estimated bias in counts. The assumption implicit in this
method is that use remains uniform over the time period of interest; if use
patterns fluctuate considerably over the season, calibration relationships
should be updated as required, and the new relationship used to calculate use
rates for that time interval.
In this example, season length was 100 days. The overall visitor use
estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).
(c) Use by category. Frequently, visitor use is described in terms of
categories, or groups, of users; the number of users in each category is
expressed as a proportion, or percentage, of the total number of users in the
sample.
Example. On the permit form 2,975 visitors indicated their method of
cooking during their visit: stoves, wood fires, or neither. Results with a 95
percent confidence interval (using χ2 procedure based on 2 degrees of
freedom) were:
Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,
95 percent confidence interval = 0.75 ± 5.99[(0.75)(0.25) / 2, 975] = 0.75 ± 0.019
= (0.731 to 0.769);
Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,
95 percent confidence interval = 0.20 ± 5.99[(0.20)(0.80) / 2, 975] = 0.20 ± 0.018
= (0.18 to 0.22);
Neither: n3 = 149, p3 = 149/2,975 = 0.05,
95 percent confidence interval = 0.05 ± 5.99[(0.05)(0.95) / 2, 975] = 0.05 ± 0.009
= (0.04 to 0.06).
(d) Use description. One variable that may be obtained by permits is
length of stay. Post stratification may also be of interest.
Example. A sample of 38 permits had an average length of stay of 2.4
nights with a standard error of 0.23 nights. This makes the 95 percent
confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).
(e) Summary-use statistics. The recreation visitor-day is defined as 12
hours of a given recreation activity performed by the associated proportion
of visitors. It is calculated as the product of the number of activity occasions
and the average amount of time spent in that activity, divided by 12.
Example. The number of permits issued for a given season was 6,750, of
which 1,232 were horse users. For horse users, there were 3.1 people per
group, and 5.2 horses per group; the estimated compliance rate was 95
percent. The total number of horse users was 3.1(1,232)/(0.95) = 4,020 people,
and 5.2(1,232)/(0.95) = 6,744 horses. The average duration of a wilderness
trip was 5 days, or 120 hours. Then, the number of recreation visitor-days for
horse users during the season was 4,020(120)/12 = 40,200.
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137
System H: Permit System With
Compliance Checks and
Mailback Questionnaires
System Description ________________________________________________
Permits are mandatory use-authorization forms issued by the agency. Use
information is determined by both the permit form and questionnaire format;
this system provides sufficient information to estimate summary-use statistics, as well as basic visit counts, visit and visitor characteristic data.
Compliance checks are required for accurate estimation of total use. Mailback
questionnaires provide supplementary information on complex nonobservable
visit characteristics. Mail surveys are much less expensive to implement
than face-to-face interviews, and the inherent problem of low response rate
can be surmounted to a great extent by planned followup. Because visitors
are responsible for obtaining permits, and because visitors fill out and return
questionnaires, visitor burden is relatively high.
Summary of System H:
Type of observations:
Measures of visitor use:
Data collection strategies:
Techniques/procedures:
Visitor burden:
Counts
Observable characteristics
Simple nonobservable characteristics
Complex nonobservable characteristics
Number of individual visits
Number of group visits
Use by category of user
Summary-use statistics
Permits
Sample plan for compliance checks
Sample plan for visitor selection for questionnaires
Permit issue
Compliance checks
Mailback questionnaires
Follow-up mailing
Estimate response rates
Moderate to high
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics to Measure
Use characteristics that can be obtained are limited only by the permit
format. Information obtained from permits can include the number of
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individuals or groups, group size, method of travel, anticipated dates of entry
and exit, length of stay, and place of residence. Mailback questionnaires
enable the permit holder to document various trip-related observations, such
as number of encounters, travel routes and destinations, actual length of
stay, and perceptions of wilderness conditions, problems and resource
conditions, past wilderness experience, knowledge of regulations and lowimpact procedures, preferences for various management strategies, and so
forth.
Step 2: Decide on a Permit Form
Standard OMB-approved permits are available for each agency. Alternatively, customized permit formats can be used. However, OMB clearance
must be obtained before the study begins if permits are to be issued in a
revised format; this includes the addition of questions to standard permit
forms. According to federal legislation, OMB clearance is required if federal
employees ask more than nine members of the public the same set of
questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the
Forest Service, application for clearance is submitted to that Agency’s
Information Systems office in Washington, DC, which forwards the application to the Department of Agriculture, and from there to OMB for final
approval. The time from initial submission to final OMB clearance is usually
about 3 months. Clearance is not required if shortened versions of the
standard permit with fewer questions are used.
Step 3: Establish a Permit-Issue Procedure
The procedure for issuing permits will be determined by (1) the reason for
issuing permits, and (2) the source of issue.
1. Reasons for Permit Issue.—Permits are issued to (a) provide a means of
public contact, (b) restrict use or categories of user, and (c) monitor use.
(a) Public contact. If the objective in issuing permits is to create
opportunities for public contact, visitors will be required to obtain permits in
person at a centralized agency facility, such as a visitor center or ranger
station. Visitor contact with a trained agency representative is valuable for
promoting the professional image of the agency and increasing visitor
knowledge of regulations, appropriate low-impact behaviors, potential hazards, and wilderness conditions. Visitors have the opportunity to discuss
possible routes and destinations within the wilderness area, and to obtain
other information of interest to them.
(b) Use restriction.—If the objective in issuing permits is to restrict use,
visitors will be required to obtain permits at a centralized agency facility,
such as a visitor center or ranger station. Alternatively, if adequate computer
facilities are available, permits can be issued from a number of different field
offices by means of a computerized reservation system so that the number of
permits available at any time can be tracked.
(c) Use monitoring.—If permits are issued with the objective of collecting accurate visitor use data, there are no associated restrictions on where
or how permits are issued. Permits may be issued by the agency or selfissued; numbers may be limited or unlimited.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
139
2. Source of Permit Issue.—Permits are usually issued by agency personnel, but may be self-issued, or distributed through a cooperative arrangement with local vendors. In the majority of cases, permits are issued from a
central location by the managing agency. Staff at local ranger stations,
information centers, or National Forest offices are responsible for issuing
permits. Occasionally, permits may be reserved; reservations may be made
by telephone or mail, or in other cases must be made in person if “no-shows”
are a problem. Reserved permits may be mailed, or held until picked up by
the visitor.
Self-issued permits are usually obtained from some convenient location. If
permits are unlimited, they may be obtained from a station located outside
the agency office or at trailheads, or from alternative locations, such as local
businesses. However, if permit numbers are limited, they must be obtained
from a central location.
If there are restrictions on certain types of user, permit-issue locations
may be placed so as to accommodate different user groups. For example, if
overnight use of a wilderness area must be rationed but day use is essentially
unrestricted, a limited number of overnight permits is made available at
some central location, whereas self-issued day-use permits are located at
trailheads.
Permits may be issued through cooperative arrangements with local
vendors or businesses. Wilderness permits may be issued by convenience
stores, bait shops, commercial outfitters, travel information centers, or
nearby campgrounds.
Step 4: Develop the Mailback Questionnaire
To be effective, a questionnaire must (1) enable managers to find out what
they want to know, (2) encourage respondents to answer, and (3) minimize
respondent burden.
There are four major steps involved in the design of an effective questionnaire: (1) question development, (2) format, (3) mailing, and (4) followup
(Dillman 1978). When in the development stages of this system, the manager
is strongly encouraged to have the questionnaire and methodology reviewed
by a social scientist from a university or the agency.
1. Question Development.—The questions asked of the visitor will be
dictated by the study objectives; that is, on the basis of what the manager
wants to know and why. Questions should be easily understood by the visitor,
they should not be too long, and there should not be too many of them. The
major principle in question development is the necessity to keep visitor
burden to a minimum. Ask only the questions necessary to meet the study
objectives, and no more.
The questions asked of the respondents will depend on what kind of
information is required to meet the study objectives. Questions can be
categorized on the basis of one or more of the following types of information:
• Attitudes: what people say they want or how they feel about something;
• Beliefs: what people think is true or false;
• Behavior: what people do;
• Attributes: what people are (personal or demographic features).
Questions must be clearly identified according to information type, otherwise responses will lead to a different type of information than that required
by the study objectives.
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The question designer is rarely a good judge of the clarity of the questions
(Ackoff 1953). Preliminary field tests are invaluable for identifying problems,
and should be conducted before the actual field surveys begin. Colleagues,
potential “users” of the data, and, if possible, a small pretest sample of
prospective respondents should fill out the questionnaire; a debriefing
session should follow to identify problems. If some inadequacy or ambiguity
becomes apparent with the set questions, questions may be added, but only
if they clarify the meaning and satisfy the requirements of step 1.
2. Format.—There are three factors to be considered in planning questionnaire format: (a) length, (b) question ordering, and (c) design and layout.
(a) Length. Questions should not be too long, and there should not be too
many of them. Questions must be worded so that respondents understand
them as the investigator wants them to; language should be simple and clear,
and there should not be too much information demanded in any one question.
If in doubt, the question should be broken into two or more questions.
The questionnaire should be as short as possible, without compromising
the study objectives, or resulting in incomplete information. A single-page
questionnaire is acceptable, but may be too short to be useful. The maximum
questionnaire length is approximately 12 pages (Dillman 1978).
Personnel may be tempted to add additional questions “just out of
curiosity”; this cannot be justified in any circumstances. Do not add questions
merely to fill up space on the questionnaire sheet.
(b) Question ordering. Questions are presented in order from simple to
complex; this is the so-called “funnel” format. Question order improves data
quality by encouraging respondents to answer because both resistance to
answering and the perceived effort involved are lessened. Once a commitment is made to answer a few questions, there is an increased likelihood that
the survey will be completed.
The questionnaire is introduced with a paragraph outlining the central
topic, the interest and importance of the topic, and its interest and relevance
to the respondent. The first few questions are the most important, as they will
determine whether the questionnaire is completed or thrown in the garbage.
The first few questions get the survey started by setting the pace and manner
of the survey, and encouraging respondents to answer. In general, initial
questions should be (1) relevant and interesting, (2) easy to answer, and (3)
applicable to all potential visitors. The first question should obviously be
related to the topic, and have socially useful implications. The questions
should be easy to answer, taking only a few seconds to understand and
answer. Therefore, long, complex and open-ended questions, and statements
requiring the respondent to express an attitude or opinion, should be
avoided. The questions should have wide applicability. Questions that
involve a category of “does not apply” or “don’t know” suggest to the
respondent that the rest of the questionnaire is equally irrelevant; this is a
major contributor to nonresponse. Simple, easy-to-answer questions include
questions about wilderness travel routes and destinations, activities participated in, group size and composition, number of other users encountered and
where, length of visit, and so on.
Subsequent questions are ordered in descending importance with respect
to the topic; topical questions are asked before questions related to personal
characteristics. Questions should be ordered so that they follow a logical
sequence. More complex questions will require some thought or judgment on
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
141
the part of the respondent; complex questions are formulated to attain
information on visitor perceptions, judgments, opinions, or attitudes. Examples are the relative importance of various aspects of the wilderness trip
in achieving “quality” wilderness experiences, attitudes toward management strategies intended to reduce visitor impact, and the acceptability of
various levels of social or resource condition impacts. Personal or confidential
questions should be placed last; these include extent of past wilderness
experience, knowledge of low-impact procedures, income and education
levels.
(c) Design and layout. Response rates are greatly affected by the details
of questionnaire design and layout. Questionnaires should be attractive,
easy to read, and look easy to do, so that respondents are motivated to
complete them. The overall design must prevent respondents from missing
or overlooking questions or whole sections.
The following design guidelines are from Dillman (1978).
• Booklet format. The questionnaire should be printed as a booklet, with
approximate dimensions of 6" x 8". If each page is typed using 12-point font
on standard 8.5" x 11" paper with 3⁄4" margins, reduction by 79 percent will
fit booklet format. The questionnaire booklet is reproduced on white or offwhite paper using good-quality printing methods; if pages are printed on
both sides, sixteen pound paper is recommended.
• Cover design. Questionnaire covers determine the overall first impression of the study, and significantly influence response rates. The front cover
must include (a) a study title, (b) a graphic illustration, (c) any needed
directions, (d) the name, address and logo of the sponsoring agency, and (e)
the identification number. The title should give an informative and accurate
impression of the study topic, make the questionnaire sound interesting, and
should be neutral (that is, it should not sound threatening or imply bias). The
illustration adds interest; it should be simple and representative of the topic.
The address of the study sponsor is important as backup information in case
respondents lose return envelopes. The name of the researcher is not
included in the address; the legitimacy of the study is endorsed by the
backing of the sponsoring agency, not by some unknown individual. The back
cover consists of a request for additional comments, and a statement of
thanks. The back cover should never include questions; because questions
are ordered, the questions that would appear there are most likely to be found
objectionable by respondents, and the probability of nonresponse is greatly
increased.
The questionnaire is identified with a stamped individual identification
number; this number corresponds to the number assigned to each recipient
on the mailing list. In general, the ID number should be placed in the upper
right-hand corner of the front cover.
• Lettering. Distinguish questions from answers by using lower-case
letters for questions and UPPER-CASE LETTERS FOR POSSIBLE
ANSWERS.
• Make questions fit the page. Questions should not continue onto the
next page. Manipulate spacing (margins, line spacing), or rearrange question
order. However, large blank spaces should be avoided.
• Identification of answer categories. Assign a number for each
answer category; this provides a convenient method of coding answers for
subsequent computer processing. Place numbers to the left of the answer
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category; this minimizes the possibility of the respondent indicating answers
other than the one intended.
• Vertical flow. Arrange answer categories and associated numbers
vertically on the page, not across the page. Vertical flow prevents the
respondent from inadvertently missing questions or sections of the questionnaire, and prevents the respondent from indicating answers other than the
one intended. The considerable spacing involved with this format gives the
impression that the questionnaire is easy to complete; a densely worded
format appears difficult.
• Instructions for answering. Specific instructions must be provided
on (a) how to provide answers (for example, “Circle number of your answer”)
and (b) how to skip screen questions. Screen questions direct a certain subset
of respondents to skip one or more questions, depending on the answer given.
Respondents can be directed by arrows to the appropriate sections of the
questionnaire.
3. Mailing the Questionnaire.—Besides the questionnaire, the two components to the mailout package include: (a) the cover letter, and (b) the
mailback, or return, envelope.
(a) The cover letter. The cover letter introduces the study to the
respondent. The first paragraph explains what the study is about, convinces
the respondent that the study is useful, and motivates the respondent to fill
out the questionnaire and return it. The study will be perceived as useful if
it is seen to meet the needs of a certain group; however, it is essential that no
bias in the researcher’s motives is apparent. The second paragraph is
designed to convince the respondent that the individual’s response is important to the success of the study. The specific individual who is to complete the
questionnaire should be clearly identified at this point. The third paragraph
is a guarantee of confidentiality. The fourth paragraph repeats the social
usefulness of the study, and contains a promise of action; for example, a copy
of the results (if requested by the respondent), an expression of willingness
to answer questions pertaining to the study (provide a telephone number and
address). Finally, the letter concludes with a statement of thanks, a closing
statement, and the sender’s name and title.
The cover letter should not exceed one page and should be printed on
agency letterhead. It should contain the date of mailing, the name, address
and telephone number of the person sending the questionnaire, and agency
affiliation. The signature should be handwritten.
(b) Return envelope. A postage-paid, pre-addressed return envelope
must be included in the questionnaire package; response rates are significantly lower if return envelopes are not provided. Business reply envelopes
should be used to avoid the use (and potential loss) of postage stamps.
4. Followup. Followup mailings are crucial for ensuring adequate response rates; without followup mailings, response rates will be less than half
of those attained by using a comprehensive followup system (Dillman 1978).
The followup procedure consists of three carefully timed mailings after the
original mailout:
(a) One week: A postcard reminder is sent to everyone. It serves as a
thank-you and acknowledgement for respondents, and as a polite reminder
for nonrespondents.
(b) Three weeks: A second package is sent out to nonrespondents. This
package contains a shorter cover letter intended to inform the nonrespondent
that their questionnaire was not received and that the individual’s response
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
143
is important to the success of the project. A replacement questionnaire and
a postage-paid return envelope are included.
(c) Seven weeks: A final mailing, similar to the second mailing, is sent
to nonrespondents. It has been recommended that this mailing should be
sent by certified mail “to emphasize its importance” to the recipient (Dillman
1978); however, the expense is considerable. Although there is some recent
evidence that certified mailings result in a substantial increase in response
rates, at least one study found that additional responses obtained by this
method had no influence on results.
Step 5: Develop Sampling Plan for Survey
When permit access is strictly regulated, permit compliance is usually very
high (over 95 percent). In this case, the entire sample population is known (in
other words, all permit holders for a given time period), and the devising of
a sampling plan is relatively simple; visitors to be surveyed are randomly
selected from the permit numbers on file (see part I, chapter 3). To increase
representation by locality, samples may be stratified by location.
Determination of the appropriate sample size (that is, the total number of
questionnaires to be issued) requires a preliminary estimate of the expected
variability in the response characteristics of interest. Preliminary estimates
are obtained from a pilot study or from data collected in previous years. A
rule-of-thumb estimate for the standard deviation is based on one-quarter of
the likely range (or minimum and maximum values) of the observations (see
part I, chapter 2). If several sample size estimates are available for different
observations, the largest calculated sample size should be used.
Step 6: Purchase Equipment and Supplies
If permits are self-issued, permit stations need to be constructed. These
stations should be both attractive and functional. Self-issue permit stations
should be designed to provide (1) a place for supplies (pencils and permit
forms), (2) a convenient, solid writing surface for the visitor to use when
completing the permit, and (3) a place to deposit completed agency copy
(normally a slot at the front). Stations may be constructed of wood or metal,
and should be set on a post at a convenient height. An attractive and easyto-read sign should be posted with instructions detailing (1) why a permit is
required, (2) who is to obtain a permit (one person or everyone in the group),
(3) where to deposit the completed agency copy, and (d) the consequences of
being found in violation.
Additional costs are associated with the printing and mailing of questionnaires. Both printing and mailing costs are influenced by questionnaire
length, the number of booklets required, stationary type and weight, method
of mail delivery, and the use of repeated mail followups.
Step 7: Obtain Mailback Responses
A well-organized system must be developed to handle questionnaire
returns. Returns must be individually coded so that the identification
number matches that on the original questionnaire; this enables returns to
be documented so that respondents who have completed questionnaires and
those requiring followup mailings can be managed accordingly. As returns
come in, they should be examined for problems which may result in missing
data (such as sticking pages, unclear directions, and so forth). The researcher
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must be prepared to handle undelivered questionnaires, and answer respondent inquiries.
Step 8: Estimate Response Rates, Compliance Rates, and Use
There are four steps in the estimation procedure: (1) estimating permit
compliance rates, (2) estimating questionnaire response rates, (3) estimating
sample sizes, and (4) estimating total use.
Estimates of permit compliance are required to determine the relationship
between the number of visitors who are in compliance with respect to the
total number of visitors actually entering the wilderness area. The total
number of visitors entering a wilderness area is estimated from the relationship between the number of permits issued, (N), and the rate of permit
compliance, (r).
Visitor use data are collected from information provided on the submitted
permit form; the collection, entry, and processing of data are therefore time
intensive and relatively expensive. Consequently, sample sizes should be
specified for each use characteristic to be evaluated categorically. Preliminary estimates of the required statistics (for example, standard deviation)
can be obtained from observations made during the permit compliance
estimation phase.
Use data are collected in accordance with the appropriate sample size and
the sampling strategy. Information obtained from permits should be sufficient for obtaining data on observable and nonobservable categories of
visitor. The number of visitors per category is expressed as a proportion or
percentage of the total number of users. However, if sample sizes are very
small, proportion data are useless for evaluation purposes. Individual and
group visit count data may be expressed as a rate (for example, number of
visitors per day), or total (for example, number of visitors for the season). In
general, totals are estimated by multiplying the “corrected” average daily
rate by the number of days in the time period of interest.
1. Estimate Permit Compliance Rates.—Permit compliance rate is estimated as the ratio of the number of permit holders (determined by the total
number of permits collected) to the total number of visitors (determined from
observer counts) during the sample observation periods.
Example. A total of 575 visitors obtained permits during the 7-day permit
compliance rate estimation phase. A random sample of n = 50 visitors
indicated that 10 did not obtain permits. Therefore, the estimated permit
compliance rate (r) was estimated as 40/50 = 0.8, or 80 percent. The total
number of users (N) for a given period is estimated by the total number of
permit holding visitors (t) divided by the permit compliance rate:
Nˆ = t / r = 575/0.8 = 719
The 95 percent confidence interval for the total is estimated by N ± 2·SE =
719 ± 2
[(575) ⋅ 50(50 − 40)] /(40)
2
3
= 719 ± 102, or between 617 and 821 visitors.
2. Response Rates.—There are several methods of calculating questionnaire response rates, (R). The first method is the ratio of questionnaires
returned to those sent out, or
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
145
R=
number returned
× 100
number sent out
However, if there is a certain proportion of ineligible respondents, or
potential respondents who could not be contacted, the formula must be
modified as follows:
R=
number returned
× 100
(number sent out) – (non - eligible + non - reachable)
(Dillman 1978).
Example. Questionnaires were sent to 200 visitors randomly selected
from permits issued for a given season. A total of 156 questionnaires were
returned. Ten contacts were ineligible and 14 could not be contacted (questionnaires were not forwarded or returned). The response rate is:
R=
156
× 100 = 88.6%
200 − (10 + 14)
3. Sample Size Estimation.—Because visitor count data are collected by
counting permits, there may be insufficient resources available to cover the
costs and time involved in the collection, input, and processing of large
amounts of data. Sample sizes for categorical data should be specified first.
Sample sizes should be estimated for each use characteristic to be measured,
and the largest (feasible) sample size is chosen. If a stratified sampling
strategy is used, stratum sample size is calculated according to whether
proportional or disproportional representation is required.
(a) Count data. The relation used to estimate sample size is:
S
n ≅ 4 ⋅
L
2
If the sampled population is small, the finite population correction (fpc) is
used to correct for overestimation bias. Using the fpc, the estimated sample
size is:
n≅
N ⋅ S2
L2 ⋅ N
S2 +
4(2) 2
where L is the width of the interval around the projected average, and N is
the size of the true population. In this case, N is the number of days in the
season. Precision is estimated by the confidence level (generally 95 percent)
and the desired width of L. For example, the investigator may wish to be 95
percent certain that the results have a precision of ± 5 percent of the total.
Operationally feasible sample sizes are obtained by varying the amount of
precision of the estimate; highly precise estimates may require sample sizes
that are too large for practical purposes.
Example. The average number of visitors observed per day during the
compliance estimation phase was 250, with S = 160. There are 100 days in
the season (N = 100). Suppose we want to be 95 percent certain that results
will have a precision of ± 5 percent, or ± 13 visitors/day. The estimated
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100(160)2
= 86. If the precision
(13 + 13)2 (100)
(160)2 +
16
is adjusted to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these
are too large or too close to the entire season of 100 days to be of practical use
due to the large underlying variance. A more reasonable level of precision
would be ± 30 percent (or ± 75 visitors per day) which would call for a sample
size of n = 15.
(b) Proportion data. Sample size (n) will be at a maximum when the
proportion of observations (p) in any given category is 0.5 (or 50 percent). The
sample size required to estimate an interval of width L around the sample
mean will be:
number of sampling days is ≈
4 ⋅ (2) ⋅ p(1 − p)
2
n=
L2
which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.
Example. Preliminary data showed that for 40 randomly selected visitors,
24 appeared to be day users. Therefore, the proportion of day users, p = 24/
40 = 0.60, and the standard error is p(1 − p) / n = (0.60)(0.40) / 40 = 0.0775.
The 95 percent confidence interval based on these data is approximately 0.6
± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size
n required for a 95 percent confidence interval with a length of at most 0.10
16(0.5)2
= 400.
(0.10)2
Therefore, it would be necessary to observe 400 visitors to obtain this amount
of precision for the estimate.
(c) Stratified sampling. If the data are stratified according to trailhead
or time block, sample sizes of each stratum must be calculated to ensure
accurate representation of the population. Sample sizes may be either
proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of
each strata or subgroup. Optimal allocation is a type of stratified sampling
where the sample size within each strata is proportional to both the size and
the variability of the sample within each stratum; the proportionality factor
(regardless of the resulting value of p) is approximately n =
[
]
is calculated as Ni ⋅ Si / ∑ ( Ni ⋅ Si ) ⋅ n. Disproportional sampling occurs when
the same size sample is drawn for each stratum (assuming equal costs to
sample each strata).
Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are
similar), whereas optimal allocation should be chosen if strata differ in the
amount of variability.
Example. In this example, data are stratified by two time blocks—
weekend days and weekdays. This stratification strategy separates out time
periods according to relative intensity of use, with the heaviest and most
variable use occurring on weekends, and relatively light and uniform use on
weekdays. For a 100-day season, there are about 72 weekdays and 28
weekend days. Suppose the available resources (budget, labor, time) dictated
that the maximum number of days that could be sampled was n = 25. The
initial value for the standard deviation for each stratum was estimated from
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147
the data obtained during the permit compliance rate estimation phase.
Sample sizes for each time block are calculated as follows:
Proportional
fb
nc
Disproportional
f
n
Optimal
allocation
f
n
Stratum
sa
Weekends
(n1 = 28)
Weekdays
(n2 = 72)
88.0
0.25
7
0.43
12
0.64
16
19.2
0.25
18
0.17
12
0.36
9
aStandard
deviation.
proportion.
cSample size.
bSampling
Because the two strata differ considerably in variability, the preferred
sampling scheme is optimal allocation; with this strategy the investigator
randomly selects 16 weekend days and 9 weekdays for data collection.
3. Use Estimation.—Use characteristics estimated with this system are
limited to individual or group visit counts. Data may be expressed in terms
of: (a) the rate (for example, number of visitors per day), (b) the total (for example,
number of visitors for the season), (c) use by category (for example, cooking
method), (d) use description (for example, length of stay), or (e) summary-use
statistics (for example, recreation visitor days).
(a) Rate of use. Suppose the number of visitors with permits for a 30 day
time period was 772. A survey of 50 visitors showed that 46 had permits for
a compliance rate of 46/50 = 0.92.The estimated number of users over the 30
day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users
per day. The estimated confidence interval for the 30 day rate is 839 ±
2 ⋅ 7722 ⋅ 50 ⋅ (50 − 46) / 463 = 839 ± 70 = (769, 909), which converts to a
confidence interval for the daily rate of (25.6, 30.3).
(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,
corrected by the estimated bias in counts. The assumption implicit in this
method is that use remains uniform over the time period of interest; if use
patterns fluctuate considerably over the season, calibration relationships
should be updated as required, and the new relationship used to calculate use
rates for that time interval.
In this example, season length was 100 days. The overall visitor use
estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).
(c) Use by category. Frequently, visitor use is described in terms of
categories, or groups, of users; the number of users in each category is
expressed as a proportion, or percentage, of the total number of users in the
sample.
Example. On the permit form 2,975 visitors indicated their method of
cooking during their visit: stoves, wood fires, or neither. Results with a 95
percent confidence interval (using χ2 procedure based on 2 degrees of
freedom) were:
Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,
95 percent confidence interval = 0.75 ± 5.99[(0.75)(0.25) / 2, 975] = 0.75 ± 0.019
= (0.731 to 0.769);
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Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,
95 percent confidence interval = 0.20 ± 5.99[(0.20)(0.80) / 2, 975] = 0.20 ± 0.018
= (0.18 to 0.22);
Neither: n3 = 149, p3 = 149/2,975 = 0.05,
95 percent confidence interval = 0.05 ± 5.99[(0.05)(0.95) / 2, 975] = 0.05 ± 0.009
= (0.04 to 0.06).
(d) Use description. One variable that may be obtained by permits is
length of stay. Post stratification may also be of interest.
Example. A sample of 38 permits had an average length of stay of 2.4
nights with a standard error of 0.23 nights. This makes the 95 percent
confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).
(e) Summary-use statistics. The recreation visitor-day is defined as 12
hours of a given recreation activity performed by the associated proportion
of visitors. It is calculated as the product of the number of activity occasions
and the average amount of time spent in that activity, divided by 12.
Example. The number of permits issued for a given season was 6,750, of
which 1,232 were horse users. For horse users, there were 3.1 people per
group, and 5.2 horses per group; the estimated compliance rate was 95
percent. The total number of horse users was 3.1(1,232)/(0.95) = 4,020 people,
and 5.2(1,232)/(0.95) = 6,744 horses. The average duration of a wilderness
trip was 5 days, or 120 hours. Then, the number of recreation visitor-days for
horse users during the season was 4,020(120)/12 = 40,200.
In 1980, permit systems were in use in 69 wilderness
areas. Of these areas, 17 limited use and 52 did not.
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149
System I: Indirect Counts
System Description ________________________________________________
With this system, various measures of use are estimated from one or more
surrogate measures of use, referred to as predictor variables. Predictors are
easier to obtain than measures of direct use, and entail less burden on
wilderness visitors. The relationship between the predictor(s) and the use
measure is quantified; once this relationship is established, it is only
necessary to monitor the predictor to obtain an estimate of the given use
characteristic. Indirect measurements can be used to predict counts and
summary-use characteristics. Relationships may be valid over several seasons; however, periodic checks should be scheduled to ensure the continued
validity of the predictive relationship. Visitor burden should decline once the
predictive relationship is established.
Summary of System I:
Type of observations:
Measures of visitor use:
Data collection strategies:
Techniques/procedures:
Visitor burden:
Counts
Observable use characteristics
Simple nonobservable characteristics
(sometimes)
Number of individual visits
Number of group visits
Summary-use statistics
Sampling plan for counter rotation (if applicable)
• spatial
•temporal
Calibration
Mechanical counters
Visual observations (cameras, human observers)
Miscellaneous data collection (weather data,
trailhead maps, and so forth)
Variable, declining.
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics
To date, the use characteristics most commonly evaluated by indirect
methods have been visitor counts, time involved in a given activity, and interparty encounter rates. The success of this method for predicting other types
of use characteristics is untested; estimates of nonobservable use characteristics may not be reliable.
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Step 2: Select the Appropriate Predictor Variable
Choice of the appropriate predictor variable is determined by several
factors: ease of measurement, predictive power, and stability (that is,
the predictive relationship should be valid for relatively long periods). The
predictor variable may be another (and easier) method of obtaining visitor
counts, such as vehicle axle counts, the number of visitor maps taken from
trailhead stations, or the campground occupancy rates. Alternatively, predictor variables may be environmental or weather factors, such as lake-water
levels, daily maximum temperature, and daily rainfall.
The predictive power of the straight-line model is estimated by the
2
coefficient of determination, or R . This is interpreted as the proportion of
observed variation in Y that can be explained by the straight-line model: the
2
higher the value of R , the better the regression model is in explaining
2
variation in Y. If R is small, the investigator will need to search for an
alternative predictor variable or variables. Pilot studies must be conducted
to evaluate the initial suitability of potential predictor variables, and whether
the relationship between the proposed predictor variable and the use characteristic of interest is sufficiently strong to be of any use as a means of
prediction.
The stability of the model is evaluated by periodic checks over one season,
or over several years. Some predictor variables may be useful for relatively
long periods, but only if use patterns do not change significantly over time.
Step 3: Select a Direct Counting Method
Visitor counts are determined by observing visitors passing a given point
at selected times. Human observers are preferable; however, cameras may be
used if calibration procedures are strictly followed (see below). Interviews
may be used to obtain information on simple nonobservable visit characteristics. To obtain information on complex nonobservable visit characteristics,
mailback questionnaires may be sent to randomly selected visitors.
Step 4: Develop a Sampling Plan for Direct Counting
The procedure for indirect methods is similar to the calibration procedures
described for systems using mechanical counters. The value of the predictor
variable is “calibrated” by direct counts, or observations, of visitors obtained
simultaneously with measures of the indirect variable so the predictive
power of the predictor variable can be assessed for its adequacy. Once the
adequacy of the predictor is established, visitor counts can be estimated from
the predictive relationship.
The amount of effort and resources expended during this phase will depend
on the required precision of use characteristic estimates, the available
resources, and the relative stability of visitor use over time. If use patterns
change substantially over the season, the predictive relationship estimated
at the beginning of the season will not be applicable later in the season; the
accuracy of the relationship must be spot checked at intervals, and updated
as required.
Use of human observers is labor intensive and expensive, but provides
highly accurate results and greater flexibility in data acquisition. Observers
may be stationed at fixed locations, such as trailheads or campsites, or
alternatively may travel assigned trail segments. For “calibration” purposes,
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
151
the minimum information to be recorded by observers includes number of
individuals, number of groups, method of travel, direction of travel, and date
and time of entry or exit. Additional information on visit or visitor characteristics may be obtained if required by the study objectives. A sample observer
recording sheet is shown in figure 1.
Sampling plans must be developed for:
1. Scheduling rotation of observers (or counters) across trailheads.
2. Calibration of mechanical counters (if applicable).
3. Visitor selection for interviews (if applicable).
Step 5: Install Equipment for Indirect Counts (If Applicable)
If cameras or mechanical traffic counters are used for measuring the values
of the predictor variable, care must be taken in equipment installation,
maintenance, and calibration. Follow manufacturer’s directions for installation, carefully test and retest the accuracy of the counter, and frequently test
battery power and sensor function.
In general, counters should be placed some distance away from the
trailhead so that only bona fide wilderness visitors are counted, and casual
visitors (those who travel only an extremely short distance) are excluded.
However, if the wilderness boundary is an extremely long distance from the
trailhead, the increase in personnel time involved in traveling to the counter
site for reading and calibrating counters may make this option untenable. We
do not advise locating counters where the trail is unduly wide (thus allowing
visitors to travel two or more abreast, and underestimating counts), or at
natural resting places (where they may mill around and cause multiple
counts). Narrow portions of the trail at locations where traffic flow is more
or less continuous offer the best count locations.
The time required for counter installation will vary according to distance
from the trailhead and counter type. After arriving at the selected site, at
least one hour will be required for counter installation. This includes time
spent examining the site, selecting the best place for counter location,
installation of the sensor and the counting mechanism, setting counter
sensitivity or delay, and testing counter operation. If a counter is mounted on
a tree trunk (as is the case for photoelectric counters), the counter will likely
shift slightly within the first day or two as a result of tree wounding; the
counter should therefore be checked, and realigned if necessary, on the
second day after initial installation. If cameras are used, additional time is
required to address privacy concerns (the camera must be located far enough
from the trail so that individuals cannot be identified in the pictures, camera
adjusted to be slightly out of focus, and so forth).
After the equipment has been installed, observe conditions for a short time
to make certain that equipment is functioning correctly, and adjust accordingly. All equipment should be labeled with agency identification, a statement of purpose, and the name, address, and telephone number of a
designated contact person. A message explaining that the camera is for
detecting use levels, and that individual identities cannot be determined,
may reduce the risk of vandalism if visitors locate the equipment.
Step 6: Collect Direct Count Data
Direct count data are generally collected by human observers. Although
labor intensive and expensive, use of human observers provides accurate
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results, and enables greater flexibility in data acquisition. Direct count data
may be obtained by observers without stopping visitors, or by observers who
stop and interview randomly selected visitors.
1. Observer Data.—It is essential that personnel are thoroughly trained in
the data collection procedures. Training ensures that observers are already
familiar with the research directives and the data collection process before
actual fieldwork begins. As a result, errors involved in the learning process
are reduced, and there will be greater consistency in identifying the sampling
units and recording responses. Training enables observers to become familiar with various contingency plans, to identify potential problems in the
research directives, and to make decisions if problems occur.
Preliminary, or pretest, fieldwork should be conducted before the actual
survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or
inadequacies in the procedures can be identified, and the consistency and
accuracy of personnel can be observed and analyzed.
Observers should be screened at intervals and their performance compared
either with each other or at different time points for the same observer;
screening provides a check on performance and identifies sources of error in
the data.
Observers may be stationed at fixed locations, such as trailheads or
campsites, or alternatively may travel assigned trail segments. If trail traffic
is low, observers may perform other tasks in the vicinity of the counter, such
as trail clearance and maintenance, visitor education, or reading; these help
pass the time and reduce observer fatigue and boredom. However, if the
observer is stationed at some distance and is observing traffic through
binoculars, it is not advisable to engage in other types of activity because of
the potential for missing visitors if attention is diverted from the trail.
Observers should be in appropriate uniform and possess necessary communication and safety equipment.
Observations must be recorded in a standardized format. The minimum
information to be recorded by observers includes number of individuals,
number of groups, method of travel, direction of travel, and date and time of
entry or exit. Additional information on visit or visitor characteristics may be
obtained if required by the study objectives. For each data sheet the observer
should record their name, the sampling location, the date, start time, the
initial counter reading, end time, and the final counter reading for that
sample period. During the sample period the observer records the number of
individuals or groups, and the time visitors pass the observation station. The
observer must be provided with sufficient data forms for the observation
period. Observers must understand the need to completely and correctly fill
out the data form; sample observations will be useless if the data collected by
the observer cannot be matched with the appropriate counter data. Observation sheets should be filed in a designated place after the observer returns to
the office.
2. Interview Data.—The interview protocol consists of five steps: (a) determining question format, (b) obtaining OMB clearance, (c) selecting and
training the interview team, (d) visitor selection, and (e) data collection.
(a) Question format. The questions asked of the visitor will be dictated
on the basis of the study objectives; that is, on the basis of what the manager
wants to know and why. Questions should be easily understood by the visitor,
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153
they should not be too long, and there should not be too many of them. Ask
only the questions necessary to meet the study objectives, and no more. The
interview should be as short as possible to minimize visitor burden.
Personnel may be tempted to add additional questions “just out of
curiosity”; this cannot be justified in any circumstances. Do not add questions
merely to fill up space on the interview sheet. If some inadequacy or
ambiguity becomes apparent with the set questions, questions may be added,
but only if they clarify the meaning and satisfy the requirements of step 1.
The question designer is rarely a good judge of the clarity of the questions
(Ackoff 1953); preliminary field tests are invaluable for identifying problems
before the actual field surveys begin.
(b) Obtain OMB clearance. According to federal legislation, clearance
from the Office of Management and Budget (OMB) is required if federal
employees ask more than nine members of the public the same set of
questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the
Forest Service, application for clearance is submitted to that Agency’s
Information Systems office in Washington, DC, which then forwards the
application to the Department of Agriculture, and from there to OMB for
final approval. The time from initial submission to final OMB clearance is
usually about 3 months.
(c) Select and train the interview team. Careful selection and training
of the personnel who are involved in collecting data are essential if the
manager or research planner is not performing the field research. The
research planner must ensure that interviews are conducted and observations collected in the manner required by the study plan.
• Personnel selection. Both personality and ability must be evaluated in
the selection process. The importance of visitor contact extends beyond the
quality of data obtained; it is an opportunity to present the image of the
managing agency. Select an interviewer who is friendly, reliable, knowledgeable, and trained in emergency procedures. Personnel should be familiar
with the wilderness area and prepared to handle requests for information
about the wilderness and the surrounding area. Many of the questions from
visitors will not be related to the interview; providing information is a
courtesy which contributes to establishing rapport with the visitors and
increases visitor cooperation. Personnel should be in appropriate uniform
and possess necessary communication and safety equipment.
• Training. It is essential that personnel are thoroughly trained in the data
collection procedures. Training ensures that observers are already familiar
with the research directives and the interviewing process before actual
fieldwork begins. As a result, errors involved in the learning process are
reduced, and there will be greater consistency in identifying the sampling
units (in this case visitors to be interviewed) and recording responses.
Training enables observers to become familiar with various contingency
plans, to identify potential problems in the research directives, and to make
decisions if problems occur.
Preliminary, or pretest, fieldwork should be conducted before the actual
survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or
inadequacies in the procedures can be identified and eliminated, and the
consistency and accuracy of personnel can be observed and analyzed. Observers should be screened at intervals and their performance compared either
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with each other or at different time points for the same observer; screening
provides a check on performance and identifies sources of error in the data.
(d) Visitor selection. Visitors are selected in accordance with the predetermined sampling plan (step 4). The location of interviews will be determined by study objectives; visitors may be interviewed upon either entry or
exit, or both. For example, if the emphasis of the study is on the effects of
group size or place of residence on wilderness use, these factors are unaffected by interview location. However, if the study objectives require information on patterns of visitor use within the wilderness area (for example,
travel or camping locations, length of stay), visitors should be interviewed as
they leave.
(e) Data collection. When interviewing visitors, personnel should begin
with a standard introduction. Personnel should give their name and agency
affiliation and the reason for the interview. For example, “Hello, I am
Marilyn Holgate. I work for the Missoula District of the Lolo National Forest.
We are trying to learn more about the use of the Rattlesnake Wilderness. It
will help us with management of the area. May I ask you a few questions
about your visit today?” After the interview, thank visitors for their time.
Responses should be recorded as they are given; interviewers should not
rely on memory to fill in the interview sheet at a later time. Make sure every
item is complete and legible; data forms must include date, time, location,
and interviewer’s name. Completed data forms should be filed in a safe place
in a central location.
Step 7: Collect Predictor Variable Data
Methods of data collection will depend on the type of predictor variable.
Count data may be logged by mechanical counters or obtained by visual
observations (either cameras or human observers). Alternative types of
predictor variables, such as environmental factors, are collected by the most
appropriate means (see below). Predictor data must be collected either
simultaneously or for the same sampling period as direct count data.
1. Counter Data.—Counts logged by the mechanical counter are recorded
at intervals determined by the appropriate sampling plan. If counters are
permanently allocated to a given location, the frequency of recording will be
determined by the calibration sampling plan. At a minimum, counts should
be recorded at least twice per month to ensure that data are not lost because
of equipment malfunction. The person obtaining count readings should check
battery power and equipment operation, and for any changes in the surrounding area which may affect count accuracy.
2. Cameras.—Record necessary observations from the developed film.
Observations must be recorded in a standardized format to minimize errors
in recording. Observations include location, date, number of individuals,
number of groups, date and time of entry or exit. Observers must understand
the need to completely and correctly fill out the data form; sample observations will be useless if the data collected by the observer cannot be matched
with the appropriate registration data. Observation sheets should be filed in
a designated place. After observations are recorded, destroy negatives and
developed photos to ensure visitor privacy.
3. Observers.—Observers should be stationed close enough to the registration station so that all traffic passing the station is accounted for; however,
they do not need to observe whether or not visitors actually register.
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155
Although observers need not be beside the registration station, they should
not wander up and down the trail. Observers do not stop visitors.
Observations are recorded on a standardized form (fig. 1). Observations
include observer name, location, date, number of individuals, number of
groups, date and time of entry or exit. Observers must understand the need
to completely and correctly fill out the data form; sample observations will be
useless if the data collected by the observer cannot be matched with the
appropriate registration data. All deposited registration forms are collected
and labeled at the end of the observation period. Observation sheets and
registration cards should be filed in a designated place.
4. Other.—Daily weather data for the location closest to the wilderness
area can be obtained from the National Weather Service. More accurate
information can be obtained from weather-recording equipment established
close to the site. If the quantity of trailhead literature (such as maps) is used
as a predictor, an observer must be detailed to monitor the station supplies
during time periods coinciding with those used for direct counts.
Step 8: Estimate Use
Linear regression is used to estimate the relationship between the predictor variable and the direct measure of visitor use; regression techniques are
described more fully in the appendix. Before calculating the regression
statistics, the data are plotted and examined for anomalies, such as excessive
curvature or scatter, which would invalidate the assumption of a straightline relationship. To predict use from values of the predictor variable,
calculate the regression relationship, Y = B0 + B1 ⋅ X , and the standard error
of the regression equation ( MSE ). The 95 percent confidence interval for
value of visitor count (Y) for a given car count (X) is approximately equal to
Yˆ ± 2 MSE where Yˆ is calculated from the regression equation.
An estimate of use for the entire season is obtained by calculating the
average number of users per day, and multiplying this estimate by the total
number of days in the season.
Example. Visitor traffic at Snow Lake Trailhead in the Alpine Lakes
Wilderness was surveyed to establish the relationship between the numbers
of vehicles in the trailhead parking lot X (predictor variable X) and the
number of visitors counted 1⁄2 mile up the trail (Y). The following data are
plotted in figure 7.
Car counts (X):
10 15 18 20 21 23 25 27 32 33 60 92 105 108 132.
Visitor counts (Y): 25 30 50 55 62 65 61 48 75 67 77 150 158 100 200.
The relationship between car counts and visitor counts was:
Yˆ = 26.48 + 1.145·X
2
with R = 0.86 and
MSE = 19.11.
The average number of cars in the trailhead parking lot was 45 per day.
Therefore, the daily number of visitors was estimated to be 26.48 + 1.15(45)
= 78. The 95 percent prediction interval for this estimate is 78 ± 38.22, or
between 40 and 116 visitors per day. Given a season length of 100 days, the
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number of users per season is estimated as 7,800, with a 95 percent confidence
interval of 4,000 to 11,600 users.
Snow Lake Data
Visitor Counts
200
150
100
50
0
10
18
21 25
32 60 105 132
Car Counts
Figure 7—Plot of visitor counts on car counts for
Snow Lake Trailhead.
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157
System J: General Visitor
Surveys
System Description ________________________________________________
This system entails the direct acquisition of information from visitors to the
wilderness area by either face-to-face interviews or questionnaires filled out
by the visitors. Use information is determined by the interview or questionnaire format, or both. This system can provide sufficient information to
enable estimates of summary-use statistics, as well as basic visit counts and
visit characteristic data. A random selection of visitors is contacted at
trailheads or other wilderness access points. Although visitors are contacted
directly, contact time is relatively low and visitor burden is moderate.
Summary of System J:
Type of observations:
Measures of visitor use:
Data collection strategies:
Techniques/procedures:
Visitor burden:
Counts
Observable characteristics
Simple nonobservable characteristics
Complex nonobservable characteristics
Number of individual visits
Number of group visits
Use by category of user
Summary-use statistics
Sampling plan for visitor selection
Interviews, questionnaires
Moderate
Operational Procedures ____________________________________________
Step 1: Decide on Use Characteristics to Measure
Use characteristics that can be obtained are determined by the question
format. Information obtained from interviews or questionnaires can include
basic descriptions of the visit (such as travel route, length of stay, and
activities participated in), and simple visitor characteristics (such as past
wilderness experience, knowledge of low-impact behavior, preference for
alternative management strategies, and so forth). If mailback questionnaires are used, information can be obtained on complex nonobservable
characteristics pertaining to the wilderness area itself, such as visitor
attitudes and visitor preferences for conditions in wilderness.
Step 2: Decide on Survey Method
Visitors are surveyed by either interviews or questionnaires, or both.
Choice of method depends on the length and complexity of the survey, the
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resources available to administer the survey (personnel, time, budget, and so
forth), the demographics of the contact population, and the location of contact
(at trailheads, at locations within the wilderness, or at their place of
residence).
1. Interviews.—Directly surveying visitors by interviews is appropriate if
the survey is relatively short, questions are simple (for example, questions
relating to attributes rather than attitudes), and budgetary resources are
limited. Interviews are especially useful if the contact population is characterized by low standards of literacy, or if there is a significant proportion of
non-English-speaking visitors.
The location of interviews will be determined by study objectives; visitors
may be interviewed upon either entry or exit, or both. For example, if the
emphasis of the study is on the effects of group size or place of residence on
wilderness use, these factors are unaffected by interview location. However,
if the study objectives require information on patterns of visitor use within
the wilderness area (for example, travel or camping locations, length of stay),
visitors should be interviewed at exit points. In general, visitors should not
be interviewed within the wilderness area, especially if surveys are long,
because personnel interruptions may be perceived as an unacceptable visitor
burden. However, if onsite responses are required, interviews may be
conducted at campsites without interfering with travel plans or disturbing
the mood of the wilderness experience.
Telephone interviews are an option if only a short time is available to
complete a study. Visitors are contacted at a trailhead and asked to supply
their name, address, and telephone number; they are contacted later by
phone. However, this method is expensive (telephone charges, interviewer
time), and has a lower response rate than other survey methods.
2. Questionnaires.—Indirect surveys by means of questionnaires are
appropriate if the survey is relatively long, questions are more complex, and
budgetary resources are sufficient for implementing questionnaire development and followup procedures (see Step 3: Formulate the Survey).
Step 3: Formulate the Survey
There are three steps in formulating a survey: (1) developing appropriate
and effective questions, (2) constructing question format, and (3) obtaining
OMB clearance. If the survey is administered by questionnaire, additional
design considerations are necessary.
When in the development stages of this system, the manager is strongly
encouraged to have the survey and methodology reviewed by a social scientist
from a university or the agency.
1. Question Development.—To be effective, the survey must (a) enable
managers to find out what they want to know, (b) encourage respondents to
answer, and (c) minimize respondent burden.
The questions are asked of the visitor will be dictated by the study
objectives; that is, on the basis of what the manager wants to know and why.
Questions should be easily understood by the visitor, they should not be too
long, and there should not be too many of them. The major principle in the
development of questions is the necessity to keep visitor burden to a minimum. Ask only the questions necessary to meet the study objectives, and no
more.
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The specific questions asked of the respondents will depend on what kind
of information is required to meet the study objectives. Questions can be
categorized on the basis of one or more of the following types of information:
•
•
•
•
Attitudes: what people say they want or how they feel about something;
Beliefs: what people think is true or false;
Behavior: what people do;
Attributes: what people are (personal or demographic features).
Questions must be clearly identified according to information type, otherwise responses will lead to a different type of information than that required
by the study objectives.
The question developer is rarely a good judge of the clarity of the questions
(Ackoff 1953). Preliminary field tests are invaluable for identifying problems,
and should be conducted before the actual field surveys begin. Colleagues,
potential “users” of the data, and, if possible, a small pretest sample of
prospective respondents should be surveyed; a debriefing session should
follow to identify problems. If some inadequacy or ambiguity becomes
apparent with the set questions, questions may be added, but only if they
clarify the meaning and satisfy the requirements of step 1.
2. Question Format.—There are two factors to be considered in planning
survey format: (a) survey length, and (b) relative order of questions.
(a) Length. Questions should not be too long, and there should not be too
many of them. Questions must be worded so that respondents understand
them as the investigator wants them to; language should be simple and clear,
and there should not be too much information demanded in any one question.
If in doubt, the question should be broken into two or more questions.
The survey should be as short as possible, without compromising the study
objectives or resulting in incomplete information. Personnel should not ask
additional questions “just out of curiosity”. Do not add questions merely to fill
up space on the questionnaire sheet. A single-page questionnaire is acceptable, but may be too short to be useful. The maximum length for mailout
questionnaires is approximately 12 pages (Dillman 1978); self-issue questionnaires should not take longer than 10 minutes to complete.
(b) Question sequence. Questions are presented in order from simple to
complex; this is the so-called “funnel” format. Question sequence improves
data quality by encouraging respondents to answer because both resistance
to answering and the perceived effort involved are lessened. Once a commitment is made to answer a few questions, there is an increased likelihood that
the survey will be completed.
The survey is introduced with a brief outline of the central topic, the
interest and importance of the topic, and its interest and relevance to the
respondent. The first few questions are the most important, as they will
determine whether the questionnaire is completed or thrown in the garbage.
The first few questions get the survey started by setting the pace and manner
of the survey, and encouraging respondents to answer. In general, initial
questions should be (1) relevant and interesting, (2) easy to answer, and (3)
applicable to all potential visitors. The first question should obviously be
related to the topic, and have socially useful implications. The questions
should be easy to answer, taking only a few seconds to understand and
answer. Therefore, long, complex and open-ended questions, and statements
requiring the respondent to express an attitude or opinion, should be avoided.
The questions should have wide applicability. Questions that involve a
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category of “does not apply” or “don’t know” suggest to the respondent that
the rest of the questionnaire is equally irrelevant; this is a major contributor
to nonresponse. Simple, easy-to-answer questions include questions about
wilderness travel routes and destinations, activities participated in, group
size and composition, number of other users encountered and where, length
of visit, and so on.
Subsequent questions are ordered in descending importance with respect
to the topic; topical questions are asked before questions related to personal
characteristics. Questions should be ordered so that they follow a logical
sequence. More complex questions will require some thought or judgment on
the part of the respondent; complex questions are formulated to attain
information on visitor perceptions, judgments, opinions, or attitudes. Examples are the relative importance of various aspects of the wilderness trip
in achieving “quality” wilderness experiences, attitudes toward management strategies intended to reduce visitor impact, and the acceptability of
various levels of social or resource condition impacts. Personal or confidential
questions should be placed last; these include extent of past wilderness
experience, knowledge of low-impact procedures, income and education
levels.
3. Obtain OMB Clearance.—According to federal legislation, clearance
from the Office of Management and Budget (OMB) is required if federal
employees ask more than nine members of the public the same set of
questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the
Forest Service, application for clearance is submitted to Information Systems in Washington, DC, which then forwards the application to the Department of Agriculture, and from there to OMB for final approval. The time from
initial submission to final OMB clearance is usually about 3 months.
4. Additional Design Considerations for Questionnaires.—If the survey is
administered in questionnaire format, additional considerations include
design, mailing, and followup procedures (Dillman 1978).
(a) Design and layout. Response rates are greatly affected by the details
of questionnaire design and layout. Questionnaires should be attractive,
easy to read, and look easy to do, so that respondents are motivated to
complete them. The overall design must prevent respondents from missing
or overlooking questions or whole sections.
The following design guidelines are from Dillman (1978).
• Booklet format. The questionnaire should be printed as a booklet,
with approximate dimensions of 6" x 8". If each page is typed using 12-point
font on standard 8.5" x 11" paper with 3⁄4" margins, reduction by 79 percent
will fit booklet format. The questionnaire booklet is reproduced on white or
off-white paper using good-quality printing methods; if pages are printed on
both sides, sixteen pound paper is recommended.
• Cover design. Questionnaire covers determine the overall first
impression of the study, and significantly influence response rates. The front
cover must include (a) a study title, (b) a graphic illustration, (c) any needed
directions, (d) the name, address, and logo of the sponsoring agency, and (e)
the identification number. The title should give an informative and accurate
impression of the study topic, make the questionnaire sound interesting, and
should be neutral (that is, it should not sound threatening or imply bias). The
illustration adds interest; it should be simple and representative of the topic.
The address of the study sponsor is important as backup information in case
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161
respondents lose return envelopes. The name of the researcher is not
included in the address; the legitimacy of the study is endorsed by the
backing of the sponsoring agency, not by some unknown individual. The back
cover consists of a request for additional comments, and a statement of
thanks. The back cover should never include questions; because questions
are in the aforementioned order, the questions that would appear there are
most likely to be found objectionable by respondents, and the probability of
nonresponse is greatly increased.
The questionnaire is identified with a stamped individual identification
number; this number corresponds to the number assigned to each recipient
on the mailing list. In general, the ID number should be placed in the upper
right-hand corner of the front cover.
• Lettering. Distinguish questions from answer choices by using lowercase letters for questions and UPPER-CASE LETTERS FOR POSSIBLE
ANSWERS.
• Make questions fit the page. Questions should not continue onto
the next page. Manipulate spacing (margins, line spacing), or rearrange
question order. However, large blank spaces should be avoided.
• Identification of answer categories. Assign a number for each
answer category; this provides a convenient method of coding answers for
subsequent computer processing. Place numbers to the left of the answer
category; this minimizes the possibility of the respondent indicating answers
other than the one intended.
• Vertical flow. Arrange answer categories and associated numbers
vertically on the page, not across the page. Vertical flow prevents the
respondent from inadvertently missing questions or sections of the questionnaire, and prevents the respondent indicating answers other than the one
intended. The considerable spacing involved with this format gives the
impression that the questionnaire is easy to complete; a densely worded
format appears difficult.
• Instructions for answering. Specific instructions must be provided
on (a) how to provide answers (for example, “Circle number of your answer”)
and (b) how to skip screen questions. Screen questions direct a certain subset
of respondents to skip one or more questions, depending on the answer given.
Respondents can be directed by arrows to the appropriate sections of the
questionnaire.
(b) Mailing the questionnaire. Besides the questionnaire, the two components to the mailout package include: the cover letter, and the mailback,
or return, envelope.
• The cover letter. The cover letter introduces the study to the respondent. The first paragraph explains what the study is about, convinces the
respondent that the study is useful, and motivates the respondent to fill out
the questionnaire and return it. The study will be perceived as useful if it is
seen to meet the needs of a certain group; however, it is essential that no bias
in the researcher’s motives is apparent. The second paragraph is designed to
convince the respondent that the individual’s response is important to the
success of the study. The specific individual who is to complete the questionnaire should be clearly identified at this point. The third paragraph is a
guarantee of confidentiality. The fourth paragraph repeats the social usefulness of the study, and contains a promise of action; for example, a copy of the
results (if requested by the respondent), an expression of willingness to
answer questions pertaining to the study (provide a telephone number and
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address). Finally, the letter concludes with a statement of thanks, a closing
statement, and the sender’s name and title.
The cover letter should not exceed one page and should be printed on
agency letterhead. It should contain the date of mailing, the name, address
and telephone number of the person sending the questionnaire, and agency
affiliation. The signature should be handwritten.
• Return envelope. A postage-paid, pre-addressed return envelope must
be included in the questionnaire package; response rates are significantly
lower if return envelopes are not provided. Business reply envelopes should
be used to avoid the use (and potential loss) of postage stamps.
(c) Followup. Followup mailings are crucial for ensuring adequate
response rates; without followup mailings, response rates will be less than
half of those attained by using a comprehensive followup system (Dillman
1978). The followup procedure consists of three carefully timed mailings
after the original mailout:
One week: A postcard reminder is sent to everyone. It serves as a thankyou and acknowledgment for respondents, and as a polite reminder for
nonrespondents.
Three weeks: A second package is sent out to nonrespondents. This
package contains a shorter cover letter intended to inform the nonrespondent
that their questionnaire was not received, and that everyone’s response is
important to the success of the project. A replacement questionnaire and a
postage-paid return envelope are also included.
Seven weeks: A final mailing, similar to the second mailing, is sent to
nonrespondents. It has been recommended that this mailing should be sent
by certified mail “to emphasize its importance” to the recipient (Dillman
1978). However, the expense is considerable; although there is some evidence
that certified mailings result in a substantial increase in response rates,
there is at least one study which found that additional responses had no
influence on the results of the study.
Step 4: Select and Train the Interview Team
Careful selection and training of the personnel who are involved in
collecting data are essential if the manager or research planner is not
performing the field research. The research planner must ensure that
interviews are conducted and observations collected in the manner required
by the study plan.
1. Personnel Selection.—Both personality and ability must be evaluated
in the selection process. The importance of visitor contact extends beyond the
quality of data obtained; it is an opportunity to present the image of the
managing agency. Select an interviewer who is friendly, reliable, knowledgeable, and trained in emergency procedures. Personnel should be familiar
with the wilderness area and be prepared to handle requests for information
about the wilderness and the surrounding area. Many of the questions from
visitors will not be related to the interview; providing information is a
courtesy which contributes to establishing rapport with the visitors and
increases visitor cooperation. Personnel should be in appropriate uniform
and possess necessary communication and safety equipment.
2. Training.—It is essential that personnel are thoroughly trained in the
data collection procedures. Training ensures that observers are already
familiar with the research directives and the interviewing process before
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
163
actual fieldwork begins. As a result, errors involved in the learning process
are reduced, and there will be greater consistency in identifying the sampling
units (in this case visitors to be interviewed) and recording responses.
Training enables observers to become familiar with various contingency
plans, to identify potential problems in the research directives, and to make
decisions if problems occur.
Preliminary, or pretest fieldwork should be conducted before the actual
survey begins. Rehearsals ensure that personnel understand procedures,
and serve as a test for the efficiency of the methods; problems or inadequacies
in the procedures can be identified and eliminated, and the consistency and
accuracy of personnel can be observed and analyzed. Observers should be
screened at intervals and their performance compared either with each other
or at different time points for the same observer; screening provides a check
on performance and identifies sources of error in the data.
Step 5: Develop a Sampling Plan
Sampling plans must be developed for:
1. Scheduling rotation of the interview teams across trailheads.
2. Scheduling interview periods.
3. Selecting visitors to be interviewed.
Step 6: Purchase Supplies
Supply costs are associated with the printing of survey forms, and the
printing and mailing of questionnaires. Both printing and mailing costs are
influenced by survey length, the number of surveys required, stationary type
and weight, and, when applicable, the method of mail delivery, and the use
of repeated mail followups.
Step 7: Collect Interview or Questionnaire Data
Survey data are collected by trained personnel in accordance with a specific
plan (as described in step 5). The interview protocol consists of (a) visitor
selection, and (b) data collection. The interviewer must be provided with
sufficient research material—data forms, writing tools, schedules, and so
forth—for the survey period. Interviewers must understand the need to
completely and correctly fill out the data forms. Interview sheets should be
filed in a designated place after the interviewer returns to the office.
(a) Visitor selection. Visitors are selected in accordance with the predetermined sampling plan (step 5). The location of interviews will be determined by study objectives; visitors may be interviewed upon either entry or
exit, or both. For example, if the emphasis of the study is on the effects of
group size or place of residence on wilderness use, these factors are unaffected by interview location. However, if the study objectives require information on patterns of visitor use within the wilderness area (for example,
travel or camping locations, length of stay), visitors should be interviewed as
they leave. Visitors should not be interviewed inside the wilderness boundary (to avoid threats to the visitor experience from management presence).
(b) Data collection. When encountering and interviewing visitors, personnel should begin with a standard introduction. Personnel should give
their name and agency affiliation and the reason for the interview. For
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example, “Hello, I am Marilyn Holgate. I work for the Missoula District of the
Lolo National Forest. We are trying to learn more about the use of the
Rattlesnake Wilderness. It will help us with management of the area. May
I ask you a few questions about your visit today?” After the interview, thank
visitors for their time. Personnel may be tempted to add additional questions
“just out of curiosity”; this cannot be justified in any circumstances.
Responses should be recorded as they are given; interviewers should not
rely on memory to fill in the interview sheet at a later time. Make sure every
item is complete and legible; data forms must include date, time, location,
and interviewer’s name. Completed data forms should be filed in a safe place.
Step 8: Obtain Mailback Responses
A well-organized system must be developed to handle questionnaire
returns. Returns must be individually coded so that the identification
number matches that on the original questionnaire; this enables returns to
be documented so that respondents who have completed questionnaires and
those requiring followup mailings can be managed accordingly. As returns
come in, they should be examined for problems which may result in missing
data (such as sticking pages, unclear directions, and so forth). The researcher
must be prepared to handle undelivered questionnaires, and answer respondent inquiries.
Step 9: Estimate Use
There are three steps in the estimation procedure: (1) estimating survey
response rates, (2) estimating sample sizes, and (3) estimating total use.
Visitor use data are collected from information provided on the survey
forms; the collection, entry, and processing of data are therefore time
intensive and relatively expensive. Consequently, sample sizes should be
specified for each use characteristic to be evaluated categorically. Preliminary estimates of the required statistics (for example, standard deviation)
can be obtained from observations made during a pilot study or similar
studies conducted elsewhere.
Use data are collected in accordance with the appropriate sample size and
the sampling strategy. Estimates of survey response rates are required to
determine the relationship between the number of visitors who are interviewed with respect to the total number of visitors actually entering the
wilderness area. The total number of visitors entering a wilderness area is
estimated from the relationship between the total number of visitors, (N),
and the rate of survey response, (r). Information obtained from survey forms
should be sufficient for obtaining data on observable and nonobservable
categories of visitor. The number of visitors per category is expressed as a
proportion or percentage of the total number of users.
1. Response Rates.—There are several methods of calculating questionnaire response rates, (R). The first method is the ratio of questionnaires
returned to those sent out, or
R = number returned × 100
number sent out
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165
However, if there is a certain proportion of ineligible respondents, or
potential respondents who could not be contacted, the formula must be
modified as follows:
R=
number returned
× 100
(number sent out) – (non - eligible + non - reachable)
(Dillman 1978).
Example. Questionnaires were sent to 200 visitors randomly selected
from permits issued for a given season. A total of 156 questionnaires were
returned. Ten contacts were ineligible and 14 could not be contacted (questionnaires were not forwarded or returned). The response rate is:
156
× 100 = 88.6%
200 − (10 + 14)
2. Sample Size Estimation.—Sample sizes for categorical data should be
specified first. Sample sizes should be estimated for each use characteristic
to be measured, and the largest (feasible) sample size is chosen. If a stratified
sampling strategy is used, stratum sample size is calculated according to
whether proportional or disproportional representation is required.
R=
(a) Continuous data. The relation used to estimate sample size is:
S
n ≅ 4 ⋅
L
2
If the sampled population is small, the finite population correction (fpc) is
used to correct for overestimation bias. Using the fpc, the estimated sample
size is:
N ⋅ S2
n≅
L2 ⋅ N
2
S +
4(2)2
where L is the width of the interval around the projected average, and N is
the size of the true population. In this case, N is the number of days in the
season. Precision is estimated by the confidence level (generally 95 percent)
and the desired width of L. For example, the investigator may wish to be 95
percent certain that the results have a precision of ± 5 percent of the total.
Operationally feasible sample sizes are obtained by varying the amount of
precision of the estimate; highly precise estimates may require sample sizes
that are too large for practical purposes.
Example. From past surveys the average amount spent per trip was $250,
with S = $160. Suppose we want to be 95 percent certain that results will have
a precision of ± 5 percent, or ± $13 per trip. If the total number of visits to a
remote trailhead was 100, then the estimated number of visits to sample is
≈
100(160)2
= 86. If the precision is adjusted to ± 10 percent
(13 + 13)2 (100)
2
(160) +
16
(or ± 25 per trip), then n = 62. Both of these are too large or too close to the
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entire group of 100 visits to be of practical use due to the large underlying
variance. A more reasonable level of precision would be ± 30 percent (or ±
$75 per visit), which would call for a sample size of n = 15.
(b) Proportion data. Sample size (n) will be at a maximum when the
proportion of observations (p) in any given category is 0.5 (or 50 percent). The
sample size required to estimate an interval of width L around the sample
mean will be:
4 ⋅ (2)2 ⋅ p(1 − p)
L2
n=
which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.
Example. Preliminary data showed that for 40 randomly selected visitors,
24 appeared to be day users. Therefore, the proportion of day users, p = 24/
40 = 0.60, and the standard error is p(1 − p) / n = (0.60)(0.40) / 40 = 0.0775.
The 95 percent confidence interval based on these data is approximately 0.6
± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size
n required for a 95 percent confidence interval with a length of at most 0.10
16(0.5)2
= 400.
(0.10)2
Therefore, it would be necessary to observe 400 visitors to obtain this amount
of precision for the estimate.
(c) Stratified sampling. If the data are stratified according to trailhead
or time block, sample sizes of each stratum must be calculated to ensure
accurate representation of the population. Sample sizes may be either
proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of
each strata or subgroup. Optimal allocation is a type of stratified sampling
where the sample size within each strata is proportional to both the size and
the variability of the sample within each stratum; the proportionality factor
(regardless of the resulting value of p) is approximately n =
[
is calculated as Ni ⋅ Si /
∑ ( N ⋅ S )] ⋅ n. Disproportional sampling occurs when
i
i
the same size sample is drawn for each stratum (assuming equal costs to
sample each strata).
Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are
similar), whereas optimal allocation should be chosen if strata differ in the
amount of variability.
Example. In this example, data are stratified by two time blocks—weekend
days and weekdays. This stratification strategy separates out time periods
according to relative intensity of use, with the heaviest and most variable use
occurring on weekends, and relatively light and uniform use on weekdays.
For a 100-day season, there are about 72 weekdays and 28 weekend days.
Suppose the available resources (budget, labor, time) dictated that the
maximum number of days that could be sampled was n = 25. The initial value
for the standard deviation for each stratum was estimated from the data
obtained during the permit compliance rate estimation phase. Sample sizes
for each time block are calculated as follows:
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
167
Proportional
fb
nc
Disproportional
f
n
Optimal
allocation
f
n
Stratum
sa
Weekends
(n1 = 28)
Weekdays
(n2 = 72)
88.0
0.25
7
0.43
12
0.64
16
19.2
0.25
18
0.17
12
0.36
9
aStandard
deviation.
proportion.
cSample size.
bSampling
Because the two strata differ considerably in variability, the preferred
sampling scheme is optimal allocation; with this strategy the investigator
randomly selects 16 weekend days and 9 weekdays for data collection.
3. Use Estimation.—Use characteristics estimated with this system are
limited to individual or group visit counts. Data may be expressed in terms
of: (a) the rate (for example, number of visitors per day), (b) the total (for
example, number of visitors for the season), (c) use by category (for example,
cooking method), (d) use description (for example, length of stay), or (e)
summary-use statistics (for example, recreation visitor days)
(a) Rate of use. Suppose the number of visitors with permits for a 30 day
time period was 772. A survey of 50 visitors showed that 46 had permits for
a compliance rate of 46/50 = 0.92.The estimated number of users over the 30
day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users
per day. The estimated confidence interval for the 30 day rate is:
839 ± 2 ⋅ 7722 ⋅ 50 ⋅ (50 − 46) / 463 = 839 ± 70 = (769, 909)
which converts to a confidence interval for the daily rate of (25.6, 30.3).
(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,
corrected by the estimated bias in counts. The assumption implicit in this
method is that use remains uniform over the time period of interest; if use
patterns fluctuate considerably over the season, calibration relationships
should be updated as required, and the new relationship used to calculate use
rates for that time interval.
In this example, season length was 100 days. The overall visitor use
estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).
(c) Use by category. Frequently, visitor use is described in terms of
categories, or groups, of users; the number of users in each category is
expressed as a proportion, or percentage, of the total number of users in the
sample.
Example. On the returned survey forms 2,975 visitors indicated their
method of cooking during their visit: stoves, wood fires, or neither. Results
with a 95 percent confidence interval (using χ2 procedure based on 2 degrees
of freedom) were:
Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,
95 percent confidence interval = 0.75 ± 5.99[(0.75)(0.25) / 2, 975] = 0.75 ± 0.019
= (0.731 to 0.769);
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Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,
95 percent confidence interval = 0.20 ± 5.99[(0.20)(0.80) / 2, 975] = 0.20 ± 0.018
= (0.18 to 0.22);
Neither: n3 = 149, p3 = 149/2,975 = 0.05,
95 percent confidence interval = 0.05 ± 5.99[(0.05)(0.95) / 2, 975] = 0.05 ± 0.009
= (0.04 to 0.06).
(d) Use description. One variable that may be obtained by surveys is
length of stay. Post stratification may also be of interest.
Example. A sample of 38 surveys reported an average length of stay of 2.4
nights with a standard error of 0.23 nights. This makes the 95 percent
confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).
(e) Summary-use statistics. The recreation visitor-day is defined as 12
hours of a given recreation activity performed by the associated proportion
of visitors. It is calculated as the product of the number of activity occasions
and the average amount of time spent in that activity, divided by 12.
Example. The number of permits issued for a given season was 6,750, of
which 1,232 were horse users. For horse users, there were 3.1 people per
group, and 5.2 horses per group; the estimated compliance rate was 95
percent. The total number of horse users was 3.1(1,232)/(0.95) = 4,020 people,
and 5.2(1,232)/(0.95) = 6,744 horses. The average duration of a wilderness
trip was 5 days, or 120 hours. Then, the number of recreation visitor-days for
horse users during the season was 4,020(120)/12 = 40,200.
A study of visitors entering the Bob Marshall Wilderness found an average
group size of 4.7; 61 percent of all groups consisted of two to four people.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
169
Groups traveling with recreational packstock are generally larger than
hiking groups.
170
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Appendices
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171
172
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Appendix A: References
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Becker, R. H.; Gates, W. A.; Niemann, B. J. 1980. Establishing
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Behan, R. W. 1974. Police state wilderness: a comment on mandatory wilderness permits. Journal of Forestry. 72: 98-99.
Bergstrom, John C.; Cordell, H. Ken; Ashley, Gregory A.; Watson,
Alan E. 1990. Economic impacts of recreational spending on rural
areas: a case study. Economic Development Quarterly. 4(1): 29-39.
Browning, James A.; Hendee, John C.; Roggenbuck, Joseph W.
1989. 103 wilderness laws: milestones and management direction in wilderness legislation, 1964-1987. In: Watson, Alan H.,
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Burde, John H.; Daum, Brian L. 1988. Day hikers at Great Smoky
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In: Gaby, Ewin D., ed. Proceedings - Ninth National Trails
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Cole, David N. 1989. Wilderness campsite monitoring methods: a
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10 p.
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206-209.
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James, George A.; Henley, Robert K. 1968. Sampling procedures for
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traffic counters to estimate recreation visits and use. Res. Pap.
SE-3. Asheville, NC: U.S. Department of Agriculture, Forest
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coastal plains of South Carolina. Res. Note SE-159. Asheville,
NC: U.S. Department of Agriculture, Forest Service, Southeastern Forest Experiment Station. 7 p.
Landres, Peter; Cole, David; Watson, Alan. 1994. A monitoring
strategy for the National Wilderness Preservation System. In:
Hendee, John C.; Martin, Vance G., eds. International Wilderness Allocation, Management and Research. Ft. Collins, CO:
International Wilderness Leadership (WILD) Foundation:
192-197.
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trails. Res. Note NE-286. Broomall, PA: U.S. Department of
Agriculture, Forest Service, Northeastern Forest Experiment
Station. 20 p.
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wilderness use from mandatory travel permits. Res. Pap. NC101. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Forest Experiment Station. 7 p.
Lucas, Robert C. 1983. Low and variable visitor compliance rates at
voluntary trail registers. Res. Note INT-326. Ogden, UT: U.S.
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patterns in the Bob Marshall Wilderness Complex, 1970-1982.
Res. Pap. INT-345. Ogden, UT: U.S. Department of Agriculture,
Forest Service, Intermountain Research Station. 32 p.
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and campsites. Res. Pap. INT-428. Ogden, UT: U.S. Department
173
of Agriculture, Forest Service, Intermountain Research Station.
12 p.
Lucas, Robert C.; Kovalicky, Thomas J. 1981. Self-issued wilderness permits as a use measurement system. Res. Pap. INT-270.
Ogden, UT: U.S. Department of Agriculture, Forest Service,
Intermountain Forest and Range Experiment Station. 18 p.
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applying the limits of acceptable change system. In: Watson, Alan
E., ed. Proceedings - Southeastern Recreation Research Conference; 1985 February 28 - March 1; Myrtle Beach, SC. Statesboro,
GA: Department of Recreation and Leisure Services, Georgia
Southern College: 1-15.
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Alan E. 1990. Attitudes toward prescribed fire policies. Journal of
Forestry. 88(7): 19-23.
McClaran, Mitchel P.; Cole, David N. 1993. Packstock in wilderness:
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INT-301, Ogden, UT: U.S. Department of Agriculture, Forest
Service, Intermountain Research Station. 33 p.
McCool, Steven F.; Braithwaite, Amy; Kendall, Kate. 1990. An
estimate of backcountry day use of Glacier National Park. Unpub.
rep. on file at University of Montana, School of Forestry, Missoula, MT.
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use in an urban forest recreation area. Res. Note NE-292. Broomall,
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Parsons, David J.; Stohlgren, Thomas J.; Kraushaar, James M.
1982. Wilderness permit accuracy: differences between reported
and actual use. Environmental Management. 6(4): 329-335.
Petersen, Margaret E. 1985. Improving voluntary registration
through location and design of trail registration stations. Res.
Pap. INT-336. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Forest and Range Experiment Station. 8 p.
Roggenbuck, Joseph W.; Lucas, Robert C. 1987. Wilderness use and
user characteristics: a state-of-knowledge review. In: Lucas,
Robert C., ed. Proceedings–National Wilderness Research Conference: issues, state-of-knowledge, future directions; 1985 July
23-26; Fort Collins, CO. Gen. Tech. Rep. INT-220. Ogden, UT:
U.S. Department of Agriculture, Forest Service, Intermountain
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Roggenbuck, Joseph W.; Watson, Alan E. 1981. Estimates of recreation use, Mount Rogers National Recreation Area, Jefferson
National Forest. Report to the Southeastern Forest Experiment
Station and the Jefferson National Forest. Blacksburg, VA:
School of Forestry and Wildlife Resources, Virginia Polytechnic
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Roggenbuck, Joseph W.; Watson, Alan E.; Stankey, George H. 1982.
Wilderness management in the Southern Appalachians. Southern Journal of Applied Forestry. 6(3): 147-152.
Saunders, Paul Richard. 1982. Monitoring and reporting recreation
use: a case study. In: Cordell, H. Ken; McLellan, Robert W., eds.
Proceedings - Southeastern Recreation Research Conference,
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NC. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southeast Forest Experiment Station: 143-163.
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Schnell, Kerry F.; Taft, Joe H. 1972. Application of remote sensing
techniques to measurement of outdoor recreation resources. PB214 638. Knoxville, TN: Tennessee University. 70 p.
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interval-count sampling. Forest Science. 21(1): 40-45.
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Margaret E.; Frissell, Sidney S. 1985. The limits of acceptable
change (LAC) system for wilderness planning. Gen. Tech. Rep.
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Daigle, John R. 1992. Visitor characteristics and preferences for
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Appendix B: Data and Data
Analysis
Observations are the raw material of any wilderness use study. Because
information gained from wilderness use studies is primarily numerical, and
because the manager is generally interested in populations or groups,
statistical methodology is required for both the characterization and analysis
of wilderness use data. In this section we describe the general types of
observations that are acquired during the research process, provide elementary methods of analyzing such data, and define the statistical meaning of
the various terms used throughout the text. The techniques presented in this
section are found in most introductory statistics texts; we review them here
in the context of monitoring wilderness use.
Variables_________________________________________________________
Variables are attributes measured by the individual observations; they are
not constant from item to item, but show variation. Variables may be either
quantitative or qualitative.
A quantitative variable can be measured and ranked. Observations on
quantitative variables may be categorized further as continuous or discrete.
A continuous variable is one which can take on virtually any possible value
within some range. Examples are distances traveled per day, and times
between wilderness trips. A discrete variable can take on only a distinct
series of values, with no intermediate values between them; they are
therefore integers. Count data are discrete variables; for example, the
number of hikers per day, the number of packstock per string.
A qualitative, or categorical, variable is one which cannot be directly
measured or ordered. Each observation is some property of the item in the
sample; these properties are classified as belonging to one of a finite number
of categories. These categories can be dealt with statistically if they can be
assigned counts or frequencies. In the simplest case, there are only two
categories required for describing all possible responses; such data are
binomial. For example, visitors classified on the basis of gender would be
either male or female. Multinomial data are described by several categories.
Examples are types of users (hikers, horseback riders, canoeists), ethnic
origin, state of residency, and so on.
Populations and Samples ___________________________________________
A population consists of all possible values of a variable. When all values
of a population are known, it follows that the population can be characterized
exactly. The various characteristics of the population, such as the population
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
175
2
mean µ and the population variance σ , are known as parameters. The
parameter has a fixed numerical value which is usually unknown to the
investigator.
A sample is a subset, or part, of the population. Sample characteristics,
such as the sample mean and the sample variance S2, are used to estimate
population parameters; a given sample characteristic is known as a statistic.
Our goal is to use characteristics of the sample to make inferences about the
corresponding characteristics of the population; thus, if the inferences are to
be valid, the sample must be representative of that population.
To ensure that a sample is representative of the population of interest, we
must employ principles of randomization. When randomly selected from a
population, each item has an equal probability of being selected. A random
sample is not haphazard, unplanned, or based on guesswork; such methods
of data selection will lead to biased results. Instead, random selection of
sample items is performed by using a random number table—a sequence of
numbers generated by a uniformly distributed random distribution. There
are two benefits to this approach. First, the selection of items is not
influenced by unknown or unsuspected biases on the part of either the
investigator or the circumstances surrounding the selection of the sample.
Second, we can apply the statistical laws of probability to infer the expected
values of an estimate and its sampling variation. A description of random
sampling and how it is performed is given in chapter 3.
Descriptive Statistics: Data Plots ____________________________________
Graphs are a quick and easy method of data analysis. Humans are
primarily visual animals; it is much easier to understand and summarize
large amounts of quantitative information when it is presented as a diagram,
rather than as a list of numbers. Data plots are a highly effective means of
(1) exploring the data set for patterns and relationships, (2) checking the data
for conformity to basic statistical assumptions if further statistical analysis
is to be performed, and (3) presenting quantitative information in as concise
and effective means as possible. In fact, plotting data is the most important
step in the analysis, and should be performed first, before more rigorous
analyses are performed.
Four basic types of data plots are considered here: (1) stem-and-leaf
displays, (2) histograms and bar charts, (3) scatterplots, and (4) time plots.
Stem-and-Leaf Displays
This type of data plot shows the frequency distribution of a single variable.
It is also useful for obtaining ranked data arrays, and for computing the
median of the sample. It is constructed by splitting the value of each
observation into two parts: the stem, which consists of one or two leading
digits, and the leaf, which consists of the remaining digits. Stem values are
listed on the left of the page, and leaf values are listed beside the corresponding stem in the order in which they are encountered.
Example. The user count data for the East Hickory Creek Trail (table 4)
consists of counts between 1 and 83. The stem would be the first digit and
the leaf the second digit; for example, the “User” count 57 (observation
number 1, week 1, day 1) would have a stem of 5 and a leaf of 7. The stemand-leaf display for the East Hickory Creek Trail user data is as follows:
176
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
0| 4556859998975577889779893879
1| 193303103513222409383540255713484108261664
2| 11871807665
3| 41633484
4| 61133571738
5| 7877873
6| 59
7| 58
8| 3
This diagram shows that the distribution of these data is highly skewed to
the right, with a few large values but with the majority of values in the lower
counts. The importance of symmetrical data distributions and corrections for
asymmetrical data are discussed next.
Histograms and Bar Charts
A bar chart is a method of showing the frequency distribution for a single
categorical or classification variable. A bar chart is constructed by first
forming a frequency table, dividing the sample into classification categories.
Bars are then drawn with height proportional to the frequency or relative
frequency of each category. Although pie charts are often used to display
categorical data, bar charts are preferred since comparison of pie slices is not
as straightforward as comparison of bars.
A histogram is another method of showing the frequency distribution for a
single continuous variable. A histogram is constructed by subdividing the
measurement axis into a number of nonoverlapping, consecutive intervals of
equal length. Each observation is contained in one of these intervals; the
number of observations in each interval is the frequency. Above each interval
a rectangle is drawn with the height proportional to the frequency (relative
frequency). The stem-and-leaf display discussed above is a rudimentary
histogram and is easily converted to a frequency table.
Example. Horse users in a certain wilderness area were asked to indicate
the type of community where they were raised. The frequency distribution for
the data are shown below; the resulting bar chart is shown in Figure 8.
Relative frequency of horse users
0.7
0.6
Farming
0.5
0.4
0.3
Country, not farm
0.2
Large town
0.1
Small town
Community type
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
City
Figure 8—Bar chart showing the relative frequency of horse users coming from different
community types.
177
Type of community
Frequency
Farming
Country, not farm
Small town
Large town
City
Relative frequency
126
59
8
16
7
0.58
0.27
0.04
0.07
0.03
Example. The user count data for the East Hickory Creek Trail (table 4)
can be presented as a frequency table (below, constructed from the raw data
or equivalently the stem-and-leaf display above) or as a histogram (fig. 9).
Class
Frequency
Relative
Frequency
1-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
>=80
28
42
11
8
11
7
2
2
1
0.25
0.38
0.10
0.07
0.10
0.06
0.02
0.02
0.01
Histogram for East Hickory Creek Users
Relative Frequency
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
70
80
90
User Count
Figure 9—Histogram showing the distribution of the daily number of users for the East
Hickory Creek Trailhead in the Cohutta Wilderness.
178
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Scatterplots
When two measurements are made on each item, a scatterplot of the paired
measurements can show the patterns in the data, or indicate the amount of
association between the two variables. Scatterplots are useful when the data
set is large, if there is a lot of variation in the data (which may mask
important relationships), and for checking the linearity of the relationship.
Scatterplots are especially critical in calibration problems where the relative
agreement between two measures must be assessed.
Example. The following data were visitor counts obtained by a mechanical
counter and by human observers at the Snow Lake Trailhead, located in the
Alpine Lakes Wilderness, Washington.
Counter:
132 514 604 107
Observers: 119 308 556 119
74 107 423 438
74 113 424 270
92 170 186 127 80.
78 180 61
8 187.
The ideal relationship between the two sets of counts would be a 1:1
correspondence between the two methods. A less desirable, but still workable, situation would be one method showing consistently higher readings
than the other.
The plot of these data (fig. 5) reveal a large amount of scatter about the 1:1
line. In general, data from human observers are more accurate than those
from mechanical counters.
Time Plots
These are similar to scatterplots, except that each observation for the
variable of interest is plotted in time order. This type of plot is extremely
useful for detecting cycles or other kinds of time-dependent patterns in the
data. It is an invaluable tool in monitoring programs, especially when the
objective is to evaluate the effects of some intervention, such as a change in
management policy or initiation of some educational program, on some
visitor characteristic.
Statistical analyses of time-dependent data are mathematically very
complex, and require considerable skill and judgment. (A very simple time
trend analysis is presented in a later section.) However, time plots are simple
to construct and can give a substantial amount of useful information which
may not be immediately apparent for the tabulated data. It should be noted
that a number of statistical methods (including the calculation of descriptives
such as the variance and standard deviation), are not appropriate for timedependent observations, and will give completely misleading results.
Example 1. Figure 4 shows a time plot of number of users monitored on the
East Hickory Creek Trail for the 112 days of the summer season. It is
immediately obvious from visually inspecting this plot that the data are
extremely cyclic. Peak numbers of users occur (not unexpectedly) on weekends, averaging about 50 per weekend day, and declining to an average of
about 10 users on weekdays. Patterns relevant to a number of management
questions (what are trail use patterns? should the trail be managed for peak
or average numbers? how are party averages affected by time in the week?
are large party sizes unusual? etc.) can be readily answered by visual
inspection.
Example 2. Figure 10 shows the number of violations committed by
wilderness visitors before commencement of an education program, and the
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179
Number of violations
18
16
14
12
10
8
6
4
2
0
0
10
20
30
40
Time (weeks)
Figure 10—The number of violations committed by wilderness
visitors before and after the initiation of a wilderness education
program.
number of violations after the program was in place. In this instance the
program appears to be effective to some extent because the number of
violations has declined. However, violations are occurring at a new steadystate level. Further management could be directed toward determining
whether the educational program is no longer effective for all visitors, or if
only a small subset of offenders needs to be targeted by an alternative
program.
It is extremely important in this kind of monitoring that there are some kind
of baseline or control measurements made before the policy or program change
to determine if the new situation actually has affected the response.
Determination of statistical differences between several series is beyond
the scope of this handbook. Competent statistical assistance should be
obtained.
Descriptive Statistics: Continuous Data _______________________________
There are several types of numerical summary measures which characterize a given data set and communicate some of its more important characteristics. The two most important attributes of a set of numbers are (1) the
location, or central value, and (2) the spread or dispersion around that central
value.
Measures of Central Tendency
The mean.—The most common measure of central tendency for a given set
of numbers is the mean, or arithmetic average. The sample mean is calculated as the sum of all the observations in the set, divided by the sample size:
n
Y + Y2 + … + Yn
Y = 1
=
n
180
∑Y
i
i=1
n
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Example. In a preliminary study of visitor impact on the Snow Lake Trail,
the numbers of visitor groups were recorded during 8 hours of observation on
each of 11 randomly selected days over the season. The data are as follows:
52, 115, 209, 46, 19, 44, 149, 158, 47, 70, 76.
11
The sum of these n = 11 observations is
∑Y
i
= 985. The sample mean is:
i= 1
11
∑Y
i
Y =
i=1
11
=
985
= 89.54
11
The median.—In a set of ranked or ordered observations (smallest to
largest), the sample median is the middle value, so that half the numbers are
less than the median value and half are greater. When the data set has an
odd number of values, there is a unique middle value among the ranked
numbers. When the data set has an even number of values the median is
calculated as the average of the two middle values in the ordered data set.
Example. For the Snow Lake Trail data, ordering gives:
19, 44, 46, 47, 52, 70, 76, 115, 149, 158, 209.
The median is therefore 70.
The median is insensitive to extremes in the data, such as very large or very
small data values. For example, if we increased the largest observation to
500, the median would be unaffected. This contrasts with the mean, which
can be markedly affected by even one extreme value.
In general, the mean and median will not be equal to each other. If the
population is skewed, the arithmetic mean will be “pulled” in the direction of
the skew. Thus, if the population is negatively skewed (where the distribution of the observations shows a pronounced tail to the left), the median will
be smaller than the mean; if the population is positively skewed, the mean
will be larger than the median. Thus, in certain cases the median may be
more appropriate than the mean for describing skewed data or outlying
observations.
Quartiles and percentiles.—The median divides the data set into two parts
of equal size. We could obtain finer resolution of our data set by dividing it
into more than two parts. Quartiles are four equal divisions of the data set,
such that the first quartile separates the lower one-quarter, or 25 percent, of
the data from the remaining three-quarters, the second quartile is the
median, and the third quartile partitions the top quarter of the data from the
lower three-quarters. Percentiles divide the data set into 100 equal parts,
such that the 99th percentile separates the highest 1 percent of the data from
the remaining 99 percent, and so on. Percentiles are not recommended unless
the number of observations is very large (>1000).
Measures of Variability
A measure of central tendency gives only partial information for a given
data set; it provides us with a measure of location but does not give any
information about the amount of variability around the location. In wilderness use studies, most investigators are interested in determining the
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magnitude of a certain outcome, or the size of the difference of that outcome
between groups. The precision of the particular sample statistic used is given
by the degree of variability in the measured outcome. Mean values should
never be given without some measure of their variability.
It is important to note that measures of variability based on random
sampling give only the effects of sampling variation on the precision of the
estimated statistics. They cannot correct for errors which are not related to
sampling; for example, biases in study design or incorrect analyses.
Range.—The simplest measure of variability is the range, which is the
difference between the largest and smallest values in a data set:
Range = max (Yi) – min (Yi)
Thus, a small range indicates a small amount of variability, whereas a large
range indicates a large amount of variability. In general, the range is
presented in terms of its minimum and maximum values, and the difference
is not computed.
Because it depends on the two most extreme values in the data set, the
range is overly sensitive to those values; the magnitudes of the intermediate
observations are ignored.
The Sample Variance and Standard Deviation.—The population variance
(denoted by σ2) is a measure of the amount of variation among the observations in a population. The sample variance S2 is calculated as the sum of
squared deviations of observations from the mean, divided by n – 1:
n
S2 =
∑ (Y − Y )
2
i
i=1
(n − 1)
2
A more accurate and computationally simpler method of calculating S is:
n
∑ Yi
n
2
Yi − i = 1
∑
n
S2 = i = 1
n−1
2
First, each observation is squared and the squared values are added together. Second, the sum of all observations is squared and divided by the
sample size n. This value is subtracted from the total of the squared
observations and this difference is divided by (n – 1). The positive square root
of the sample variance is called the sample standard deviation (S); it is one of
the most important descriptive statistics. S can be thought of as a measure
of how far a typical observation deviates from the average.
If the sample comprises more than 5 percent of the population (assuming
sampling is done without replacement), the S2 is too large, on average. To
correct this problem, multiply by the finite population correction factor (fpc),
defined as (N – n)/N.
Example. For the Snow Lake Trail data, the sum of all n = 11 observations
11
was
∑ Yi = 985, and the sum of squared observations was
i= 1
2
Then the sample variance S was calculated as:
182
11
∑Y
i
2
= 124, 073 .
i=1
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
S2 =
124, 073 −
10
(985) 2
11 = 3, 587.0727
Since the season at Snow Lake is roughly 100 days, a sample of 11 days
exceeds the 5 percent rule, so the estimated variance needs to be adjusted
2
using the fpc. S = 3,587.0727 (100 – 11)/100 = 3,192.495. The square root of
this corrected estimate of the population variance is the sample standard
deviation, S = 3, 192.494 = 56.5.
The Standard Error .—An investigator rarely studies every member of the
population, but only a small representative sample. The mean calculated
from such a sample consists of observations drawn at random from the
population; therefore, there is nothing distinctive or unusual about this
sample or its mean. If another sample were selected, chance alone almost
always produces a sample consisting of different observations and consequently a different sample mean. Each randomly drawn sample has a mean,
and each sample mean is an estimate of the true (but unobservable)
population mean. If it were possible to calculate the means of all possible
samples of a given size from a population, we would obtain a distribution of
sample means whose values would differ from one another, but would cluster
around the true population value. The standard deviation of the population
of all possible sample means is called the standard error. The standard error
quantifies the variability of the sample means relative to the true population
mean, or the certainty with which we can estimate the true population mean
from the sample. The standard error quantifies the precision with which the
sample mean estimates the true population mean.
The standard error of the mean (SE) is computed for a simple random
sample as:
SE =
Standard deviation
sample size
Example. For the Snow Lake data, the estimated standard error of the
mean is:
SE = 56.5/ 11 = 17.03.
Confidence Intervals .—A confidence interval is the range of values for the
mean that can be considered feasible for the population. The width of a
confidence interval depends partly on the standard error (and therefore on
both the standard deviation and the sample size), but also on the amount of
“confidence” we wish to associate with the resulting interval. The investigator selects the degree of confidence to be associated with the confidence
interval. A 95 percent confidence interval is the most common choice,
although smaller or larger confidence intervals can be computed according
to the degree of confidence required. If a 95 percent confidence level is
specified, approximately 95 percent of such intervals will correctly contain
the unknown population mean. This also means that about 1 in 20 such
intervals (5 percent) will not contain the unknown population mean.
A value from Student’s t distribution is multiplied by the estimated
standard error when n is smaller than 30. For sample sizes of 30 or more, the
multiplier is selected from the standard normal (or z) distribution. For most
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183
practical purposes, 2.0 is an adequate approximation for the multiplier to
construct a 95 percent confidence interval.
Procedure: For a given confidence level, the confidence interval for a
population mean is calculated from the mean Y the sample size n, and the
standard deviation S. Recall that SE = S/ n . Then the 95 percent confidence
interval is approximately:
(Y − 2 ⋅ SE, Y + 2 ⋅ SE)
Example. For the Snow Lake data, n = 11, Y = 89.54, and S = 56.5. The
degrees of freedom associated with the estimate of S are (11 – 1) = 10. The
approximate 95 percent confidence interval is given by 89.54 ± 34.06 = (55.48
to 123.61).
Descriptive Statistics: Categorical Data _______________________________
Much of the data describing wilderness visit and visitor characteristics are
categorical. That is, each observation in a sample belongs to one of a finite
number of groups or categories. In the simplest case, such data are binomial;
there are only two categories required for describing all possible responses.
For example, a visitor classified on the basis of gender would be either male
or female. Multinomial data are described by several categories; examples
are ethnicity (white, African-American, Hispanic, Native American, etc.),
marital status (single, married, divorced, widowed, separated), state of
residence, and so on. Such data cannot be summarized by the statistics used
for continuous data, such as mean and standard deviation. For example, if
ethnic groups were classified into 10 groups labeled from 1 to 10, an “average”
ethnicity code would be meaningless. Instead, the investigator is interested
in the number of items in each category, expressed as a proportion or
percentage of the total number of observations; measures of central tendency
and spread can be calculated for data expressed in this form. The value of the
total should always be presented when proportion data are used. However,
if the sample size is very small, proportion data will be useless for evaluation
purposes.
Binomial Data
Assumptions for binomial sampling require that observations are independent; that is, each element of the population has an equal probability of being
selected, and selecting any particular observation does not influence the
outcome or selection of any other observation. Furthermore, the overall
proportion of observations having the feature of interest must not change
during the sampling process.
In the simplest case, a given variable can be described in terms of two
possible outcomes; one outcome specifies individuals which have the feature
of interest (“successes”, or YES = 1), and the other outcome specifies
individuals which do not have that feature (“failures”, or NO = 0).
Sample Calculations.—Let p represent the proportion of “successes.” For a
random sample of size n, the average or expected number of “successes” is n·p.
Then, where there are X individuals having the feature of interest:
p = X/n
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In other words, p is a mean of a set of observations that are either 0 or 1. The
standard error for the proportion of “successes”, SEp, is calculated as the
square root of the product of the proportion of “successes” p and the
proportion of “failures” (1 – p), divided by the sample size:
SEp =
p(1 − p)
n
Confidence Intervals.—The 95 percent confidence interval for a proportion
p may be approximated for most practical purposes by:
p ± 2·SEp.
Example. A survey of 100 randomly selected wilderness visitors reported
that 36 visitors used a campstove. Let p denote the proportion of all visitors
who used a stove. Then p = X/n = 36/100 = 0.36 and the estimated standard
error of p is
p(1 − p)
=
n
0.36(1 − 0.36)
, or 0.048.
100
The approximate 95 percent confidence interval for p is:
p±2
p(1 − p)
= 0.36 ± 2 (0.36)(0.64) / 100
n
or (0.266 to 0.454).
The length of the 95 percent confidence interval is 0.188, or about 19
percent. Suppose we wish to increase the precision of this estimate to 10
percent. Then the sample size necessary to obtain a 95 percent confidence
interval with this amount of precision is:
4(2)2 (0.36)(0.64)
n≈
= 369
(0.10)2
Multinomial Data
Multinomial responses are an extension of the simpler binomial case.
Instead of only two possible outcomes, each observation results in one of k
possible outcomes, where k is a number greater than two. For example,
suppose we determine that there are three types of wilderness users: hiker,
horseback rider, and mountain biker. There are thus k = 3 possible outcomes,
or categories, for each visitor. A multinomial analysis would involve classifying each of n visitors who entered the wilderness area into one of the k = 3
categories.
Sample calculations : There is probability pi that an observation will occur
in category i. For k categories, there will be ni observations in each category,
k
and the sum of all observations
∑n
i
= n.
i=1
Recall that in a two-category (binomial) situation, the expected number of
“successes” and the expected number of “failures” are n·p and (1 – p)n
respectively. Similarly, in a multinomial situation, the expected number of
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185
observations resulting in category i is n·pi where i = 1, 2, ..., k categories, and
the expected number of “failures” is (1 – pi )n.
Confidence Intervals.—The 95 percent confidence interval cannot be approximated by 2·SE. Instead, the formula used to calculate the confidence
interval for the expected or mean values of each pi is:
2
pi ± χ α,
k − 1 ⋅ SEi
2
where χ α,k−1
is the 100(1–α)th percentile of a chi-square (χ2) distribution, with
(k –1) degrees of freedom, and the standard error calculated for each category
pi (1 − pi )
.
n
Example. A survey of n = 100 wilderness visitors reported three user type
categories: hikers, mountain bikers, and horseback riders. They observed
n1 = 67 hikers, n2 = 25 horseback riders, and n3 = 8 mountain bikers. The
proportions of each type of user were as follows:
is SEi =
ni
pi
Hikers
Horse users
Mountain bikers
67
p1 = 67/100
= 0.67
25
p2 = 25/100
= 0.25
8
p3 = 8/100
= 0.08
To obtain the simultaneous 95 percent confidence intervals for p1, p2, and p3,
we use the tabulated value of χ 32 –1= 2, 0.95 = 5.99. The 95 percent confidence
intervals are given by:
(0.67)(0.33)
p1 : 0.67 ± 5.99
= (0.56 to 0.79)
100
(0.25)(0.75)
p2 : 0.25 ± 5.99
= (0.14 to 0.36)
100
(0.08)(0.92)
p3 : 0.08 ± 5.99
= (0.013 to 0.15).
100
Differences Between Variables ______________________________________
In the previous section we demonstrated the procedures for estimating a
given population parameter by using sample statistics; we evaluated the
precision of that estimate by calculating confidence intervals. However,
many wilderness problem situations involve the detection of differences
between some observed value and some other value, either historical or
maximum allowable use levels, or values derived from previous studies. In
this section we discuss the procedures for testing for differences between two
values.
When evaluating differences between values, in effect we are evaluating
the competing claims of the two values as to which estimate of the value is
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the correct one for the population, or alternatively, how well the two values
agree. Methods for deciding between these competing claims are called
hypothesis testing.
Detailed information on hypothesis testing procedures are given in a
number of statistical texts (for example, Neter and others 1985, Snedecor and
Cochran 1980, Steel and Torrie 1980). For our purposes it is important to note
that there is a close relationship between the use of a confidence interval and
a hypothesis test. We can infer the result of the hypothesis test at a level of
statistical significance associated with the confidence interval. For example,
a value falling outside of the 95 percent confidence interval calculated for the
difference between two sample means indicates that there is a statistically
significant difference between the sample means at the α = 0.05 level. This
is generally interpreted as a decision to reject the null hypothesis of no
difference between sample values. However, presenting differences in terms
of confidence intervals is more informative than expressing the probability
level of statistical test of significance. Generally, the investigator is more
interested in determining the magnitude of the difference rather than a
single arbitrary decision value for statistical significance; confidence intervals produce a range of values for the population value of the difference
(Gardner and Altman 1986).
Determination of sample sizes necessary to detect specified differences is
similar to procedures discussed previously. Those interested in further
details are encouraged to consult either a statistician or a statistical text.
One-Sample Tests
A one-sample test is appropriate if interest centers on detecting departures
of the sample estimate (calculated from the data) from some null, or
reference, values. For example, reference values may be historical use levels
or maximum allowable use levels. The null hypothesis is that there is no
difference between the observed mean and the reference value; that is
(Observed Mean Use Level = Historical Use Level). If the historical mean
value lies outside the confidence interval constructed around the sample
mean, then the equality hypothesis is rejected.
The procedure for comparing a sample proportion p to a reference proportion p0 is similar. For the null hypothesis that p = p0, if p0 falls outside the
confidence interval for p, then the null hypothesis is rejected.
Procedure:
1. Identify the parameter of interest (for example, the mean, proportion,
etc.) to be estimated, and describe it in the context of the wilderness
“problem” to be evaluated.
2. Determine the null value; that is, the historic value, the maximum
acceptable value, the regulatory or legislated value, or other reference value
of interest.
3. Calculate the mean and standard error for the sample data.
4. Calculate a confidence interval for the parameter of interest (the
population mean or proportion).
5. If the reference value falls outside the confidence interval, the hypothesis is rejected.
Example. In a certain wilderness area prior to 1985, horses were the only
type of packstock used; the average daily number of horse-user groups up to
that time was 20. However, after 1985, llama use became more prevalent.
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The manager wishes to determine whether or not the prevalence of horse use
has changed from “historical” levels. The null hypothesis is that (Current
Horse Use = 20).
Sample data for the number of horse-user groups collected for 10 randomly
selected days over a single season were:
17, 9, 6, 5, 6, 34, 7, 21, 6, 4.
The sample mean X = 11.5, n = 10, SD = 9.67, and the reference mean is 20.
Then the 95 percent confidence interval for the mean is 11.5 ± 2·(9.67/
10 = (5.38, 17.62). Because the value of 20 falls outside (above) the 95
percent confidence interval for the current horse use, the manager concludes
that the prevalence of horse use measured during this particular season is in
fact lower than historical levels. However, this year may be atypical in some
way; for example, unusually bad weather or economic conditions may have
adversely affected the numbers of horse users. To determine if this observation is actually a trend toward lower horse use in general, the manager will
have to obtain data for several more seasons.
Comparing Two Samples
The investigator may be interested in detecting a difference between the
means of samples from two different populations. Examples include detecting differences between current values for population and “baseline” measurements for the sampled population, or measurements made at a different
location or under different circumstances.
For evaluating the difference between two independent samples, estimates
of the difference between the population means and an estimate of the
standard error for that difference are required. The null hypothesis is that
there is no difference between means. The standard error for X – Y is
estimated by the square root of the sum of the squared standard errors for
each of the two means:
SEX − Y =
S12 S2 2
+
n1
n2
The 95 percent confidence interval for the difference between two means is
approximated by:
X − Y ± 2 ⋅ SEX − Y
The samples are judged to be significantly different if the confidence interval
does not contain 0.
Evaluating the difference between population proportions is similar; the
null hypothesis is that the difference between the population proportions is
zero. The standard error for the difference is estimated by:
SE p1 − p2 =
p1 (1 − p1 ) p2 (1 − p2 )
+
n1
n2
The 95 percent confidence interval for the difference is approximated by
p1 − p2 ± 2 ⋅ SE p1 − p2 .
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Procedure:
1. Identify the parameter of interest (for example, the mean, proportion,
and so forth), and describe it in the context of the wilderness “problem” to be
evaluated.
2. Calculate the sample estimates of the mean or proportion for both
groups.
3. Calculate the difference between sample estimates.
4. Calculate the standard error for the difference of the sample estimates.
5. Calculate the confidence interval for the difference between the population means.
Example. At Snow Lake wilderness area, group counts were obtained over
an 8-hour period for each of 12 randomly sampled days in 1990 and 11
randomly sampled days in 1991. These counts produced the following data:
1990: 148, 138, 45, 62, 123, 340, 273, 92, 231, 205, 115, 107.
1991: 52, 115, 209, 46, 19, 44, 149, 158, 47, 70, 76.
The null hypothesis is that there is no difference in mean group size between
years.
For the 1990 sample, n1 = 12, X = 156.58 and S = 88.62; for the 1991 sample,
n2 = 11, Y = 89.55, and S = 59.89. The difference between the sample means
is X – Y =156.58 – 89.55 = 67.03. The estimated standard error for this
difference is:
SE p1 − p2 =
(88.62)2 + (59.89)2 = 31.31.
12
11
The 95 percent confidence interval for the difference is 67.03 ± 2(31.31) = (4.4,
129.7). The value 0 falls outside the 95 percent confidence interval; therefore,
the data casts doubt on the veracity of the hypothesis of no difference between
1990 and 1991 use levels. In other words, mean group size in 1991 was
significantly smaller than group size in 1990.
Comparing More Than Two Samples
Analysis of Variance.—The analysis of quantitative data obtained from
more than two samples is usually performed by the procedure known as
analysis of variance, or ANOVA. The independent variable whose effect on
the response is to be studied is the factor under study (sometimes referred to
as the treatment), and the different subpopulations, or components, are the
levels of that factor.
Example. The manager of a given wilderness area wishes to determine
the effects of four types of travel methods (hiking, rafting, horseback riding,
mountain biking) on total distance traveled by visitors. The response is total
distance traveled. The factor is travel method. The levels are the types of
travel methods; hiking, rafting, horseback riding, and mountain biking each
constitute a level.
Example. The manager wishes to determine whether the relative location
of registration stations affects the number of visitors actually registering.
Three locations were tested: at the trailhead, at a fixed distance down the
trail (one-quarter mile from the trailhead), at a “natural” stopping place (on
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189
top of an incline). The response is the number of completed registration cards
as a proportion of the total number of visitors passing the registration
stations. The factor is station location. The levels are the three location
categories.
In these examples the factor is qualitative, and the levels correspond to
different qualitative attributes or categories of the factor. Factors may also
be quantitative; in these cases the levels are described by a numerical
quantity on a scale (for example, age in years, number of years of education).
Analysis of variance determines whether or not there are differences in the
true averages associated with the different levels of the factor. If the null
hypothesis is rejected, this is interpreted to mean at least two of the mean
responses are different. The test statistic is the ratio of factor variance to the
common variance—the F-statistic. The calculated F-value is compared to the
critical F values which are tabulated in the back of many statistical texts. The
appropriate critical F is determined by the number of degrees of freedom
associated with the numerator and denominator of the ratio. As a general
rule of thumb, when F is close to 1, the null hypothesis cannot be rejected (the
average responses are similar for all groups), and if F is much larger than 1
(as determined from the appropriate table of F values), then the null
hypothesis is rejected (at least one mean is different).
The calculations used to obtain the calculated F-statistic are performed by
using formulae similar to those used to calculate the single sample mean X
2
and sample variance S . Because these calculations are fairly involved,
standard computer statistical packages are used.
Analysis of variance techniques are outside the scope of this handbook. For
more information, the reader is encouraged to consult Neter and others
(1985), or other statistical texts.
Comparison of Proportions .—A common requirement of many wilderness
studies is the comparison of count or frequency data when observations can
be classified according to two or more different factors. This class of problems
occurs when there are R populations divided into C categories. The table that
displays the observations is called a two-way contingency table. In these cases
we wish to determine whether various categories are statistically independent; that is, if the proportions observed for all categories are similar to
expected values. Under the hypothesis of statistical independence, the row
(or column) classification is not influenced by the column (or row) classification. Under this hypothesis the distribution of the cell frequencies within any
given row (or column) are proportional to the overall column (or row)
frequencies. Examples are comparisons of patterns of use between day hikers
and overnight hikers, or the proportions of wilderness users from an urban
background who ride horses versus those that hike.
The test statistic used to perform this test is the chi-square (χ2) statistic:
χ =
2
∑
all cells
(Observed – Expected)2
Expected
The observed cell counts are the number of observations in each cell. The
expected cell counts are calculated as: (rth row total)·(cth column total)/n,
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where n is the total number of observations. The χ2 value calculated by this
formula is compared to the critical tabulated value; the appropriate χ2 is
selected with reference to a given probability α (usually 0.05), and the
appropriate degrees of freedom. The number of degrees of freedom used to
calculate the critical value are (R – 1)·(C – 1) if there are R rows and C
columns. If the calculated χ2 value is larger than the critical value, the null
hypothesis of independence between row and column classifications is
rejected.
Confidence intervals for individual cells or for differences between cells
may be computed as described previously for multinomial proportion data.
Procedure:
1. Tabulate the sample count data according to their respective group R
and category C; these are the observed cell counts.
2. Calculate the row and column totals.
3. Calculate the expected cell counts.
4. Determine the appropriate degrees of freedom (R – 1) and (C – 1).
2
2
5. Calculate χ , and compare to the tabulated value of χ with (R – 1)(C – 1)
degrees of freedom.
6. Calculate confidence intervals for any or all differences.
Example. A wilderness manager wished to determine whether use patterns of different categories of users changed as a result of a certain specified
management action. The use category was length of stay; categories of use
were specified as “short-term” (under 4 hours), “intermediate” (over 4 hours
but not overnight), and “overnight.” The response was visitor number. A
randomly selected baseline sample of 240 visitors was obtained and classified
before the management action, and 200 randomly selected visitors were
classified after the action. The data are:
Type of use
Before action
After action
Total
Short term
Intermediate
Overnight
72
120
48
80
70
50
152
190
98
240
200
N = 440
Column totals
The expected cell counts are:
Type of use
Short term
Intermediate
Overnight
Column totals
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Before action
After action
Total
(152)(240)
= 82.91
440
(152)(200)
= 69.09
440
152
(190)(240)
= 103.64
440
(190)(200)
= 86.36
440
190
(98)(240)
= 53.45
440
(98)(200)
= 44.55
440
98
240
200
440
191
2
The calculated χ statistic is:
χ
2
2
2
2
72 − 82.91) (80 − 69.09) (120 − 103.64)
(
+
+
=
+
82.91
+
69.09
103.64
(70 − 86.36)2 (48 − 53.45) 2 (50 − 44.55)2
+
+
86.36
53.45
44.55
= 1.436 + 1.723 + 2.582 + 3.099 + 0.556 + 0.667= 10.063
with (R – 1)(C – 1) = (3 – 1)(2 – 1) = 2 degrees of freedom. The critical χ22, 0.95
= 5.992. Because 10.063 > 5.992, we conclude that there was a difference in
use as a result of the management action.
To pinpoint which of the three types of users were affected by the management action, we can perform either of two tests:
(1) Calculate combined χ2 values for each row, and compare to the critical
2
χ2 with (C – 1) = (2 – 1) = 1 degrees of freedom. The critical χ 1,0.95 = 3.84. The
difference between “before” and “after” groups within each user type is
significant if χ2calculated > χ2critical. The χ2 values for each of the three user
categories were, respectively:
Short term:
1.436 + 1.723 = 3.183 < 3.84.
Intermediate: 2.582 + 3.099 = 5.681 > 3.84.
Overnight:
0.556 + 0.667 = 1.223 < 3.84.
(2) Calculate the approximate 95 percent confidence intervals for the
differences in proportions for each of the user categories (the formula is given
in the section Multinomial Data). The difference between “before” and “after”
groups within each user type is significant if the value 0 lies outside the
interval.
The proportions for each cell are:
Type of use
Short term
Intermediate
Overnight
Before action
0.30
0.50
0.20
After action
0.40
0.35
0.25
Difference
–0.10
0.15
–0.05
The confidence intervals for each difference (by user type) are:
Short term: (–0.19 to –0.01)
Intermediate: (0.06 to 0.24)
Overnight:
(–0.13 to 0.03).
Therefore, the intermediate users were strongly affected by the management
action, showing a statistically significant decline in numbers. Short-term
users were marginally affected by the management action, showing a slight
increase. Overnight users were relatively unaffected.
To further isolate differences between observed and expected frequencies,
the individual contributions to the overall chi-square test statistic may be
compared to a critical chi-square value with 1 degree of freedom, 3.843. For
this example the largest cell contribution is 3.099 which is smaller than
3.843. This means there are no individual cells with observed frequencies
that differ significantly from their expected frequencies under the null
hypothesis of independence of the row and column classifications.
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Association of Two Variables ________________________________________
This section describes methods of association analysis where the variation
in one variable is used to account for the variation in another variable and to
predict (or forecast) values of that second variable. There are four basic
types of association analyses. Regression specifically uses the value of one
variable to predict the value of the other. Regression techniques are most
frequently used for obtaining indirect measures of hard-to-measure use
characteristics as a function of more easily measured variables; they are
occasionally used in calibration applications. Correlation analysis examines the strength of the linear relationship between two continuous variables. Calibration is the assessment of the relative agreement of two
independent measures of the same use characteristic. In its simplest form,
trend detection looks for relationships as a function of time. Compliance
estimates are a form of “calibration”; supplementary observations are used
to adjust visitor counts for the bias occasioned by visitors failing to comply
with the mandatory permit or voluntary registration systems.
An introduction to the basic concepts of association analyses are given
below. Detailed discussion of these topics is beyond the scope of this manual;
interested readers should consult Neter and others (1985), Steel and Torrie
(1980), or other statistical texts for further information.
Regression
The simplest relationship between two variables X and Y is a straight line.
The data comprising X and Y are a set of pairs (x, y); Y is the dependent
variable (the variable to be explained) and X is the independent (or explanatory) variable. The general relationship between Y and X is given by:
Ye = β0 + β1·X
where Ye is the expected, or mean, value of Y; β0 is the intercept, or value of
Y when X = 0; and β1 is the slope of the relationship, or the change in Y for
a unit change in X. There are specific assumptions regarding the distributions of each variable, the most important of which is that X, being the
independent variable, can be determined with little or no error relative to Y;
this is the fundamental assumption of any linear regression problem.
Therefore, the investigator must be very clear about which variable can in
fact be defined as the independent variable.
The intercept is estimated by:
b0 = Y − b1 ⋅ X
The slope is estimated by:
n n
∑ Xi ∑ Yi
n
i =1
XiYi − i =1
∑
n
b1 = i =1
2
n
∑ Xi
n
2
Xi − i =1
∑
n
i =1
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
193
The percentage variation explained by the regression of Y on X is:
∑ (Yˆ − Y )
n
R2 =
2
i
i=1
n
∑ (Y − Y )
2
i
i=1
where Yˆi is the estimated value obtained from the fitted regression; that is,
2
Yˆi = Y + b1 ( Xi − X ) = b0 + b1·Xi. The value of R is always between 0 and 1. The
2
square root of R is the correlation coefficient R, which should be given the
same sign as the regression coefficient, b1.
Most modern spreadsheets such as Excel, Lotus, or Quattro provide for
regression analysis. As part of their summary output an analysis of variance
(ANOVA) table is generated, similar to the one produced for comparing
∑ (Y − Y )
n
several groups. The sources of variability are: SSTotal =
i
2
=
i=1
∑ (Y − Yˆ ) and SSRegression =
n
SSRegression + SSError where SSError =
2
i
i
i=1
∑(
n
i=1
)
2
Yˆi − Y . Note that given any two sums of squares the third may be
computed by addition or subtraction. An alternate formula for SSError is
(1 – R2)SSTotal. The degrees of freedom for SSRegression for a simple linear
model is 1 since there is a single predictor variable. The degrees of freedom
for SSError is (n – 2). Dividing the SSError by the degrees of freedom for error
gives the Mean Square Error, abbreviated MSE (i.e., MSE = SSError/(n –
2)). As before, an F ratio is computed by changing sums of squares into mean
squares and then forming their ratio, i.e., F = (SSRegression/1)/(SSError/
(n – 2)). The hypothesis that β1 = 0 is rejected if the calculated F ratio exceeds
the appropriate table value with 1 and (n – 2) degrees of freedom.
In many analyses of wilderness use, the investigator wishes to predict the
anticipated response for some given value of X. The mean response is
calculated simply by plugging in the given value of X into the regression
equation and calculating Y. The 95 percent confidence interval for this new
observation of Y is:
2
1
X new − X
Ynew ± 2 ⋅ MSE 1 + + n
2
n
Xi − X
∑
i=1
(
(
)
)
An essential first step in the analysis of regression data is to examine a
scatterplot of the data. The nature of the scatter will show whether there is
in fact a linear relationship between the two variables. If the relationship
between X and Y is positive or increasing from left to right, b1 will be positive,
and if the relationship is negative or decreasing from left to right, b1 will be
negative.
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
Multiple regression models consist of two or more independent variables
that are used to predict the dependent variable. See Neter and others (1985),
Steel and Torrie (1980), or other statistical texts for details on computation
and inference.
Example. Visitor traffic at Snow Lake Trailhead in the Alpine Lakes
Wilderness was surveyed to establish the relationship between the numbers
of vehicles in the trailhead parking lot (indicator variable) and the number
of visitors counted 1⁄2 mile up the trail (Y). The data were:
Visitors
25
30
50
55
62
65
61
48
75
67
77
150
158
100
200
Snow Lake Data
200
150
Visitor Counts
Cars
10
15
18
20
21
23
25
27
32
33
60
92
105
108
132
100
50
0
10
18
21 25
32 60 105 132
Car Counts
Example of the sample relationship between
number of cars and visitors.
The relationship between car counts and visitor counts was:
Y = 26.48 + 1.15 X
2
with r = 0.86. That is, the mean number of visitors increases by 1.15 for every
additional car, and 86 percent of the variation in direct visitor counts could
be explained when car counts are considered.
The summary statistics for this relationship are:
n
n
i=1
i=1
n = 15, X = 48.07, ∑ X i = 721, ∑ X i 2 = 57, 663,
n
n
n
i=1
i=1
i=1
∑ Yi = 1, 223, ∑ Yi2 = 134, 651, ∑ XiYi = 85, 139.
134, 651 − (26.48)(1, 223) − (1.15)(85, 139)
= 19.11.
13
The average number of cars in the trailhead parking lot was 45 per day.
Therefore, the associated number of visitors was estimated to be 26.48 +
1.15(45) = 78. The 95 percent prediction interval for this estimate is:
Then
MSE =
78 ± 2(19.11) 1 +
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
1
(45 − 48.07) 2
+
= 78 ± 39 = (39, 117).
15 57, 633 − 7212 / 15
195
Correlation
Rather than predict the value of Y from X, we may be interested only in
determining the strength of the linear association between the two variables.
Correlation analysis does not assume a cause-and-effect relationship between X and Y.
The correlation between two variables is expressed as a coefficient (the
correlation coefficient r), rather than an equation. The value of r does not
depend on which variable is designated X and which is Y; neither is it affected
by the units in which X and Y are measured. The correlation coefficient
always takes on a value between –1 and +1. If r is near 0, this is interpreted
as the absence of a linear relationship; it does not necessarily mean that there
is no relationship at all. A “strong” correlation is implied if |r| ≥ 0.8, a
correlation is “weak” if |r| ≤ 0.5, and a correlation is “moderate” if 0.5 < |r|
< 0.8. However, if the association between the two variables is curved, the
calculated r will underestimate the true strength of the relationship; conversely, r will be too high if several observations are different from the rest.
Therefore, it is critical to examine a scatterplot of the data before attempting
to interpret the practical significance of r.
Example. The correlation between car counts and visitor counts is:
r=
0.86 = 0.93.
Calibration
An important part of all wilderness use studies is the evaluation of the
reliability of different methods of data collection. In general, reliability is
assessed by comparing two methods of measuring a given use characteristic;
calibration is the determination of how well the two measures agree. For
example, it is a common practice to evaluate the effectiveness of mechanized
counters for obtaining visitor traffic counts by comparing readings to data
collected by human observers. In these cases, one method (for example,
human observers) is known to be highly accurate, but is relatively expensive;
the other method may be cheaper and less time intensive to operate, but the
accuracy is unknown or variable. The investigator uses the two different
methods to obtain a simultaneous measure of a given use characteristic (the
observations are therefore paired). If agreement between the two methods is
high, the cheaper method can be substituted with no loss of accuracy.
Alternatively, there may be no agreement between methods, indicating that
no substitution is possible. A third alternative is that the data obtained from
the new method show consistent deviations from the values obtained by the
original method. The bias associated with the new method can be quantified,
and the cheaper method substituted for the old, with the data adjusted by the
appropriate correction factor.
There are several cautions to be observed when collecting and analyzing
calibration data:
1. The purpose of calibration is to assess the differences between paired
observations; this means the observations must be true pairs. For example, if
observations from human observers are to be used to check the accuracy of
a mechanical counter, human observers must take data for the same location
and for the same time periods as the mechanical counters. Suppose the
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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
working day of the human observer is only 8 hours, but the mechanical
counter can run day and night. The counts made by the mechanical counter
outside the working hours of the human observer should not be included in
the analysis.
2. It is not correct to compare two methods by either (a) evaluating the
means and standard errors of each group separately, or (b) calculating the
correlation between methods. Using these analyses to evaluate the relative
merits of two different methods is completely misleading. A calibration
problem has only one randomly selected set of visitors, but two observations
are made for each individual visitor.
Comparing separately calculated means and standard errors implicitly
assumes that there are two randomly sampled populations. The correlation
coefficient is actually a test of how likely it is that the two variables are not
related at all; on the other hand, variables in a calibration problem are
obviously associated by their very nature.
3. Many errors of analysis and interpretation can be avoided by plotting the
data first.
These last two points can be demonstrated by a simple example. Suppose
A and B represent two methods of obtaining visitor count data. Figure 11
shows two situations where (a) there is little agreement between the two
methods, and (b) agreement is good, but method B gives consistently higher
readings than method A. Method A and method B can be summarized by the
same respective means and standard errors in both instances! However,
visual inspection of these data leads us to conclude that in the first case the
two methods do not agree and no substitution is possible; no further analysis
is required. In the second case, methods A and B appear to agree, but
estimates obtained from B would require adjustment by a constant correction factor; further calculations are performed to obtain the correction factor
and the associated precision.
The major assumption underlying all calibration techniques is that the
original relationship calculated for the calibration data remains the same
over the duration of the season. This will not be true in practice. For example,
visual calibration devices such as cameras may be triggered by leaves
blowing across the sensors, which will be more of a problem in autumn. The
Calibration Example 2
80
80
70
70
60
60
Method B
Method B
Calibration Example 1
50
40
50
40
30
30
20
20
10
10
0
0
10
20
30
40
50
60
70
0
0
10
20
Method A
30
40
Method
MethodBC
50
60
70
Figure 11—Hypothetical examples of patterns of visitor count data
obtained by two methods. Example 1 shows poor agreement between
methods. Example 2 shows good agreement between methods.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
197
sensitivity of the trigger device will be affected by battery aging and failure.
To assure accuracy in count data, calibration should be performed at
frequent intervals and, if possible, whenever the power source is changed,
and/or the trigger devices are altered.
The easiest method of calibrating or comparing two counting methods is to
first plot the data. The method considered most accurate is plotted along the
vertical axis and the candidate method is plotted along the horizontal axis.
A regression line may then be fitted to the data. If the slope is not significantly
different from zero, then there is no relationship between the two methods
and the candidate method should be discontinued. If the intercept (bo) is
nonzero, then there is an inherent bias between the two methods.
Consider the scatter plots in Figure 11.Methods A and C are to be evaluated
as more efficient or less costly alternatives to Method B. Figure 11A shows
no relationship between the two figures, and in fact the R2 value is 0.02, much
too close to 0 to indicate a useful relationship. The F ratio is 0.25, much less
than any critical value with 1 and 12 degrees of freedom. Figure 11B on the
other hand shows a fairly strong relationship, and in fact the R2 value is 0.94
with an F ratio of 189.84. However the intercept is computed as 13.26,
meaning that Method C is underestimating the count obtained by Method B
by about 13 individuals. Because this is a strong relationship, knowing the
count using Method C, we can predict with good accuracy what the Method
B count would be.
198
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
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| File Type | application/pdf |
| File Title | Wilderness recreation use estimation: a handbook of methods and systems..use estimation: a handbook of methods and systems |
| Subject | RMRS-GTR-56 |
| Author | USDA Forest Service - RMRS |
| File Modified | 2002-03-11 |
| File Created | 2001-05-03 |