2120-0744 Part B 2013

Equation Chapter 1 Section 1

Supporting Statement

Human Response to Aviation Noise in Protected Natural Areas

OMB Control Number 2120-0744

B. Collections of Information Employing Statistical Methods

The agency should be prepared to justify its decision not to use statistical methods in any case where such methods might reduce burden or improve accuracy of results. When Item 17 on the OMB Form 83-I is checked "Yes", the following documentation should be included in the Supporting Statement to the extent that it applies to the methods proposed:

1. Describe (including a numerical estimate) the potential respondent universe and any sampling or other respondent selection method to be used. Data on the number of entities (e.g., establishments, State and local government units, households, or persons) in the universe covered by the collection and in the corresponding sample are to be provided in tabular form for the universe as a whole and for each of the strata in the proposed sample. Indicate expected response rates for the collection as a whole. If the collection had been conducted previously, include the actual response rate achieved during the last collection.

Project Rationale

Data from this collection will be used to develop regression models that quantify relationships between visitor responses to aircraft noise (per the survey instruments) and in-situ noise exposure, measured simultaneously by trained professionals. These relationships will be used to predict visitor response and set noise-impact thresholds for use in Air Tour Management Planning. As such, the data will be used to predict percentage response of all recreational visitors exposed to aircraft noise in National Park Units covered by the National Parks Air Tour Management Act (see Supporting Statement A for a full discussion of the Act’s relevance to the proposed research effort).

Guided by extensive analysis of data from previous dose-response studies, ^{i,ii, iii, iv, v} as well as policy and park management considerations expressed by the agencies, we have identified the following parameters of primary importance to these regression models:

• Aircraft noise exposure (independent variables)¹

• LeqAll: Aircraft equivalent (energy-average) sound level, normalized to the visit duration

• PEnHelos: Percentage of aircraft acoustic energy due to air-tour helicopters

• PEnProps: Percentage of aircraft acoustic energy due to air-tour propeller aircraft.

• Visitor responses (dependent variables)

• Annoy: Annoyance from aircraft noise

• IntWithNQ: Interference by aircraft sound with Natural Quiet and sounds of nature.

As documented in Supporting Statement A, both visitor-response variables are measured through a variety of survey questions, using both uni-directional response scales (“Extremely Annoyed” to “Not at all Annoyed”) as well as bi-directional response scales (“Extremely Annoyed” to “Extremely Pleased”).

As noted in Supporting Statement A, noise from air tour overflights is a key management issue in the National Parks. Previous research on the response of national park visitors to aircraft noise has been limited in one major respect: responses were obtained at only a limited subset of park activities and site types. To generalize to all ATMP situations, additional activities and site types are needed. In addition, while multiple survey techniques have been utilized for previous research, they have not been performed in the same parks and sites to allow for robust comparison of efficacy and utility.

Project Purpose

In more detail, the proposed survey effort expands on previous work in three ways:

1. Low aircraft activity at previously studied site types. For previously studied site types (frontcountry overlooks and short hikes), it provides additional data for low aircraft activity, to (1) obtain statistical significance of one-or-more additional (physically important) aircraft noise metrics and (2) thereby better justify future application to low-aircraft-activity time periods. These additional data will also increase the number of sites for each site type, to enable better comparisons of site types among park units—thereby more precisely determining site-to-site variability.

2. New site types. It increases the number of site types represented in the survey collection by extending survey collection to activities/site types not previously studied (frontcountry day hikes and historical/cultural sites, backcountry day hikes and multi-day hikes, and camp sites)—thereby determining these site-type “offsets” from the two site types in the current database. In this way it includes different visitor experiences from those previously measured, including multi-hour and multi-day visits.

3. Multiple survey instruments. It simultaneously tests multiple survey instruments in the same settings to compare methodologies. This robust comparison of methodologies will allow researchers to identify the strengths and weaknesses of each instrument and provide the means for selecting the best survey instrument to support park management policy decisions, on a park-by-park basis.

Inference Population

The goal of this research is to produce regression models of aviation noise dose-response relationships—models that are empirically valid and generalizable to all National Park visitors exposed to aircraft noise. More than 285 million people visited national parks and other units of the National Park Service during 2009.^vi Of these, about 64 million were recreational visits to parks in the Air Tour Management Plan program.

Potential Respondent Universe and Selection Method

The respondent universe will be English-speaking individuals 18 years of age and older who visit specific study areas in National Parks, and engage in specific activities such as viewing scenic/ natural/historical features, observing wildlife, short-duration hiking (for one to two hours), day-hiking (more than two and generally fewer than eight hours), taking limited backcountry excursions (overnight hikes/camping), or participating in ranger-led activities.  On each survey day, teams of trained surveyors will be stationed at each selected point during typical visitation hours, which may be site and/or park dependent. The surveyors will recruit study participants by contacting as many visitor groups as possible based on surveyor availability.

Survey Frames

The proposed research will inform the development of Air Tour Management Plans (ATMPs). The primary survey frame for this research consists of the approximately 100 parks that require ATMPs (see Appendix B-1 for map of ATMP parks). For the proposed research, we will conduct surveys at approximately eight of these ATMP parks. In order to achieve sufficient dose measurements, we will impose a secondary survey frame by selecting study parks from among those that have a minimum average of one air tour overflight per day (365 per year). This provides us with 26 parks from which to choose (see Appendix B-2 for parks and overflight volumes).

We will coordinate with the National Park Service to select parks that represent the geographic distribution and available activity types of the ATMP parks as a whole, to ensure that the regression models resulting from this research are generalizable to our inference population. This coordination also will help ensure the acceptability of our results to NPS park managers, who sometimes maintain that all parks/sites are unique. Survey collection will take place over two field seasons, anticipated to include summer/fall 2010 and spring/summer/fall 2011.

2. Describe the procedures for the collection of information including:

   • Statistical methodology for stratification and sample selection,

   • Estimation procedure,

   • Degree of accuracy needed for the purpose described in the justification,

   • Unusual problems requiring specialized sampling procedures, and

   • Any use of periodic (less frequent than annual) data collection cycles to reduce burden.

Estimation and Inference Methods

For consistency with past studies, this proposed study will use model-based estimation and inference methods—more specifically multi-level logistic regression. Our ongoing re-analysis of all relevant past data (not yet completed or published) has successfully employed such regression analysis to model visitor response as a function of aircraft noise exposure and statistically significant mediator variables. In essence, these additional data will expand the current database and will justify its expanded applicability.

Description of the Regression Model

The newly acquired data will expand our ongoing analysis into several new site types (see later tables). That ongoing analysis regresses six visitor responses to aircraft noise (two response questions, combined with three dichotomizations), against a total of seven statistically significant predictors (three aircraft noise doses and four mitigating variables, including site type). That analysis will be essentially repeated with these newly acquired data.

In brief, estimation will consist of multi-level logistic regression models, guided by techniques in Gelman and Hill (2007).^vii In more detail, the previously successful regression model was:

1\* MERGEFORMAT ()

In this multi-level logistic regression:

1. Response (in percent) is one of the six response/dichotomization combinations investigated: the two responses listed above, dichotomized as SomewhatOrMore, ModeratelyOrMore, and VeryOrMore – all of which refer to respondents’ stated level of annoyance in response to aircraft noise.

2. The logit, Z, contains nine fixed-effect terms: the logit’s intercept, the basic noise metric (LeqAll²), two supplemental noise metrics that proved significant (PEnHelos³ and PEnProps) plus their interaction, and four significant mitigating variables (SiteType, ImpNQ_VorMore,⁴ AdultsOnly, and SiteVisitBefore).

The coefficients of each of these contain both a deterministic and a normal random component.

3. In addition, the logit contains the two multilevel “random-effects” terms (also normal), which the multilevel software also determines from the data.

This same model, sometimes with one or two additional predictors, is planned for this current effort. In more detail:

1. Low aircraft activity at previously studied site types. To satisfy the first Project Purpose (see page 2), we intend to augment this regression model with one or two additional acoustic metrics that are sensitive to low aircraft activity—e.g., the percent time that tour aircraft are audible (PTAudTours).

2. New site types. To satisfy the second Project Purpose, we intend to augment the categorical predictor, SiteType, to include additional factors for the newly measured site types. Of main interest is the site-type "offset" between the new site types and the two already studied: frontcountry overlooks and short hikes. Of secondary interest is whether the other functional dependencies in the prior dose-response relations remain valid, or perhaps require generalization or modification for these new site types.

3. Multiple survey instruments. To satisfy the third Project Purpose, we intend to compare responses to similar questions among the three survey instruments. In that way, we will learn the comparability of the three instruments (and their respective noise-exposure methods) in measuring nominally the same response.

Variance Estimates and Inference Methods

Sample selection and sampling unit

This research is intended to guide decision making at National Parks for which the National Park Service and Federal Aviation Administration intend to develop Air Tour Management Plans (ATMPs), and at which there are sufficient air tours to provide a range of aircraft noise exposure against which visitor response can be regressed. Therefore, our selection of parks and sites will be informed by the ATMP program (see Appendix B-1: Map of Current ATMP Parks). In addition, as discussed above, study parks will be selected that are representative of the geographic distribution and activity types of parks nationally. Furthermore, survey collection locations within parks will be selected in coordination with National Parks Service personnel at the national and local level. To ensure that the park visitors we survey are representative of the universe of park visitors, we will take the following steps:

• English-speaking visitors over 18 will be intercepted and surveyed. The surveyors will determine English proficiency from initial conversations they have upon first contact with park visitors.

• Survey collection will take place five to seven days per week, to account for variation between weekday and weekend visitors and aircraft overflight activity.

• Survey collection will occur during typical visitation hours, which may be site and/or park dependent—to account for overflight variation during early morning, mid-morning, afternoon and perhaps sunset.

• Survey collection will be performed at a variety of site types and specific sites, to capture the range of activities in which visitors participate.

Prior empirical dose-response research in national parks (cited in the Project Rationale section, above) revealed no significant effects attributable to characteristics of sub-groups within the population (i.e., demographics). Therefore, the sampling for the proposed research will not be stratified.

The sampling unit for this collection is the individual park visitor. Table 1 describes our anticipated sampling: first parks, then sites, then visitors (respondents).

This table represents our best estimate of the expected number of surveys we will collect in this study, and our burden hour estimate (15 minutes per respondent, 4200 hours per Supporting Statement A, Question 12) is based upon this expected number.

TABLE 1: Survey Collection Plan, including expected number of respondents for two years of sampling.

Site types previously measured	Park area	Site types	Target sampling sizes
			Parks	Total sites (see note 1)	Respondents per site, per survey instrument	Respondents per survey instrument	Total Respondents
Yes	Frontcountry	Short hikes Overlooks	3	7	175	1,225	3,675
No	Frontcountry	Day hikes Historical sites	5	10	175	1,750	5,250
	Backcountry	Day hikes Multi-day hikes Campgrounds	3	15	175	2,625	7,875
TOTALS (see note 2)			11	32	-------	5,600	16,800
Note 1: Total sites split more-or-less evenly among the parks and site types.

In further explanation of this table, each selected park will contain several selected sites, depending upon the park type and its availability of desired site types. In all, we expect a total of 11 parks, some with only one site type and some with multiple site types—for an expected total of 32 sites (as tabulated).

As the table shows, we intend to sample these 32 sites separately in two site-type groups (those previously measured and those not), to conform with two of the purposes of this effort. We currently anticipate sampling 7 sites for the two previously studied site types combined, plus 25 sites for the 5 new site types combined.

Note that some of the new site types may have lower visitation rates than overlook and short-hike types. Nevertheless, we intend to extend survey collection, as required, to fulfill our target of 175 respondents for each site, per survey instrument.

The original application for this data collection proposed that surveys would be conducted over the course of a 20-day period (average) at each of the parks surveyed, depending upon aircraft activity and high- or low-visitation rates. Based on the data collection experiences to date (see below), we believe this continues to be an accurate schedule. We will allow additional time for setup, breakdown, weather and other unforeseen factors that may prevent survey collection on certain days. Survey collection will be extended to fulfill our target requirements for number of observations, if necessary.

This data set will enable a robust analysis of within-park and among-park variance, for all the site types at which we administer surveys (see below for representative sample-size calculations).

Selection probabilities

Because surveyors will not know in advance how many visitors will arrive at each site, random sampling of visitors (e.g., interviewing every third visitor) will not be possible; to do so would risk not obtaining a sufficient sample. Therefore, the selection probability for each visitor to a survey site will be 100%, subject only to interviewer availability.

Our target of 175 respondents per site per survey instrument is consistent with results achieved in our previous studies, ^{e.g., ii} which surveyed visitors at a more limited number of site types and specific sites. In addition, our target accommodates reasonably foreseeable response exclusions due to lack of noise exposure data or errors in response (e.g., unreadable, damaged or inappropriately completed surveys). Based on previous research results, we anticipate that our target number of observations will be more than adequate to support the planned multilevel regression—as well as auxiliary, bivariate statistical comparisons.

Survey Collections to Date

To date, we have collected 4,640 surveys in 4 national parks, as shown in Table 1B, for an estimated burden of 1,160 hours.

TABLE 1B. Summary of survey data collected to date.

Park	Site	Day-Hike	Overnight Hike	Short-Hike	Cultural- Historic
Grand Canyon	Hermit Trail	449	135
Grand Canyon	Grandview Trail	291	126
Grand Canyon	Tusayan Ruins				374
Zion	Taylor Creek	453
Zion	West Rim Trail	182	127
Bryce Canyon	Fairyland Trail	1102
Glacier	Hidden Lake Trail	181		335
Glacier	Sperry Trail	540	345
	Total	3198	733	335	374	4640

Survey Response Rates to Date

Survey response rates are provided in Table 1C. The “overall response rates” are calculated as the total number of respondents who agreed to take the surveys, as a percentage of the total number of park visitors “intercepted” by our survey teams, and invited to participate. The “completed survey response rates” reflect the same pool of respondents who agreed to participate, but remove those respondents who did not end up completing the surveys. The average response rates across all survey instruments and sites are shown in the bottom row of Table 1C. The weighted averages reflect each study site’s contribution to the total sample collected to date.

TABLE 1C. Survey Response Rates to Date

Sample Size Calculations in Support of Table 1

Preface concerning the three survey instruments

The three survey instruments are the products of three separate scientific groups that have been gathered together by the Volpe Center into one combined project. Each separate group has its specialized survey methods, acoustical measurement-or-synthesis methods—as well as its own analysis methods. The analysis methods that accompany each survey instrument differ in their mathematics and their tested conclusions. For this reason, each group will analyze its own instrument, independently.

To calculate sample size, we provide details here for only the first survey instrument (referred to as “The human response to aviation noise - visitor survey, version 1” in the Collection Instruments section of Supporting Statement A). This instrument employs more alternative responses and more predictors in its dose-response mathematics than do the other two instruments. Its analyses will, therefore, most likely require more data points than the other two. It is for that purpose that we chose it for these sample-size calculations. Our target sample sizes, given below, should therefore provide more-than-adequate samples for the other two survey instruments, as well.

Sample partitioning among parks, sites and visitors

Sample size calculations hinge upon the results of the previous analysis. Since that work is still ongoing and not yet reported, we include extra detail here.

In the prior analysis the regression model of Eq.(1) was fit within the “R” Statistics System, using the function lmer() in the package lme4.^viii Below is the “R” output for one of those ongoing regressions—the response/dichotomization of “Annoy_ModeratelyOrMore”, which is of particular interest for ATMP application:

Generalized linear mixed model fit by the Laplace approximation

Formula: "Annoy_MorMore ~ (1|Park) + (1|Site) + 1 + SiteType + LeqAll + PEnHelos + PEnProps + SiteVisitBefore + AdultsOnly + I(PEnHelos * PEnProps) + ImpNQ_VorMore"

AIC BIC logLik deviance

1514 1573 -745.8 1492

Random effects:

Groups Name Variance Std.Dev.

Site (Intercept) 0.0152672 0.123560

Park (Intercept) 0.0067854 0.082374

Number of obs: 1572, groups: Site, 9; Park, 4

Fixed effects:

Estimate Std. Error z value Pr(>|z|)

(Intercept) -4.0838577 0.3667824 -11.134 < 2e-16 ***

SiteTypeShortHike 1.1275413 0.2063434 5.464 4.64e-08 ***

LeqAll 0.0158053 0.0083092 1.902 0.05715 .

PEnHelos 0.0083059 0.0026081 3.185 0.00145 **

PEnProps 0.0066900 0.0029056 2.302 0.02131 *

SiteVisitBeforeYes 0.5513902 0.1699233 3.245 0.00117 **

AdultsOnlyYes 0.1855097 0.1569553 1.182 0.23723

I(PEnHelos * PEnProps) 0.0001063 0.0000916 1.161 0.24567

ImpNQ_VorMoreYes 0.7627218 0.1481054 5.150 2.61e-07 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:

(Intr) StTySH LeqAll PEnHls PEnPrp StVsBY AdltOY I(PE*P

StTypShrtHk -0.194

LeqAll -0.614 -0.104

PEnHelos -0.198 -0.133 -0.363

PEnProps -0.238 -0.027 -0.243 0.727

SitVstBfrYs -0.141 0.001 0.048 -0.002 -0.030

AdltsOnlyYs -0.297 -0.105 0.003 0.002 -0.018 0.057

I(PEnH*PEP) 0.026 0.059 -0.015 -0.180 -0.318 0.051 -0.002

ImpNQ_VrMrY -0.317 0.030 0.020 -0.001 -0.008 -0.012 -0.031 0.001

Note the following: The AdultsOnly predictor was accepted in this regression for consistency with the other regressions, in which it was more significant. The interaction term was accepted because it made its two additive terms more physically (acoustically) realistic.

In this regression, specific park and specific site are the two random-effect (multilevel) parameters. By using multilevel methods with these two parameters, we learn the prediction uncertainty of our results for future application to single parks, single sites—one at a time—without underestimating that uncertainty.

To partition proposed additional data points intelligently by park and site, we need to determine, from this output, the relative uncertainty variances for park, site and visitor (respondent).

These three variances derive from the regression’s logit in Eq.(1), repeated here:

2\* MERGEFORMAT ()

Mathematically, the variance of Z is straightforwardly computed with an adaption of equation E.3 from the ISO Guide: ^ix

3\* MERGEFORMAT ()

where C_i are the regression coefficients within Z, Var[C_i] are the uncertainty variances of those coefficients, and is the coefficient correlation matrix. The first line in this equation is valid because multilevel regression considers variances at the three levels (park, site, and visitor) to be independent.

Park and site uncertainty variances are directly tabulated in the input: Var[parks]= 0.00679, Var[sites]= 0.0153. These variances derive from the standard mathematics of multilevel regression, when park and site are entered as “random effects”—that is, “levels”—in the regression. Note that these are the “unexplained” variances, after the regression controls for aircraft noise levels and all significant mitigating variables. Before control, these park and site variances were much larger.

Determining Var[visitors] requires evaluation of the two summation terms in Eq.(3). As is apparent from the equation, this visitor variance depends upon the coefficient variances and their mutual correlations—as well as the particular values of the predictors (if they appear as a result of a partial derivative). Because the logit is “linear” in the coefficients, each partial derivative equals that coefficient’s predictor value— e.g., and so forth. And the partial derivative of C₀ equals unity.

As with any regression, the residual variance is a minimum at the predictor centroid. At that centroid, all the predictor values in Eq.(3) equal zero, so only the variance of the logit’s intercept, C­₀ , remains.

To most easily obtain that minimum variance, we recompute the regression after centering all the predictors—including the categorical ones, which we center by converting them to 0’s and 1’s —then averaging over all data points, and then centering on that average. Note that we can do this even for the SiteType categorical variable, since it has only two factors. This results in the following “R” output (without the now-unnecessary correlation matrix):

Generalized linear mixed model fit by the Laplace approximation

Formula: "Annoy_MorMore ~ (1|Park) + (1|Site) + 1 + SiteType + LeqAll.c + PEnHelos.c + PEnProps.c + SiteVisitBefore.c + AdultsOnly.c + I(PEnHelos.c * PEnProps.c) + ImpNQ_VorMore.c"

AIC BIC logLik deviance

1514 1573 -745.8 1492

Random effects:

Groups Name Variance Std.Dev.

Site (Intercept) 0.0152672 0.123560

Park (Intercept) 0.0067854 0.082374

Number of obs: 1572, groups: Site, 9; Park, 4

Fixed effects:

Estimate Std. Error z value Pr(>|z|)

(Intercept) -2.080e+00 1.799e-01 -11.567 < 2e-16 ***

SiteTypeShortHike 1.128e+00 2.063e-01 5.466 4.61e-08 ***

LeqAll.c 1.581e-02 8.313e-03 1.901 0.057244 .

PEnHelos.c 1.124e-02 3.057e-03 3.677 0.000236 ***

PEnProps.c 1.319e-02 4.691e-03 2.811 0.004935 **

SiteVisitBefore.c 5.514e-01 1.700e-01 3.244 0.001179 **

AdultsOnly.c 1.855e-01 1.569e-01 1.182 0.237157

I(PEnHelos.c * PEnProps.c) 1.294e-04 9.129e-05 1.418 0.156214

ImpNQ_VorMore.c 7.627e-01 1.481e-01 5.151 2.59e-07 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Therefore the relevant (controlled) error variances at the data centroid are:

• Park: 0.0068

• Site: 0.0153

• Visitor: 0.0324 (square of 0.1799).

Next we multiply the centroid-visitor variance by a factor of 9, to convert it to an approximate “off-centroid” value—obtaining 0.13. This factor of 9 is based upon regression plots and their 95% prediction uncertainty bounds from the ongoing analysis. Then the relevant (controlled) error variances of the data centroid are:

• Park: 0.0068

• Site: 0.0153

• Visitor: 0.32.

Then ignoring incremental costs for the moment, the most efficient way to reduce error variance for future measurements is to sample in proportion to these variances:

• 2.25 sites/park

• 20 visitors/site.

Adjustment due to expected good-data rate. Our past study resulted in a good-data rate of 60%. Most of the data drop-out was caused by our physical inability to adequately measure various metrics of aircraft noise—at particular times of day, or under adverse weather conditions, or under adverse (second-by-second) ambient-noise conditions. A much smaller part of the drop-out was due to incomplete questionnaires (for visitors who did consent to the interview).

This data drop-out occurred automatically in our regression calculations, whenever a visitor was lacking one of the regression predictors.

Since we anticipate the same good-data rate for future measurements, we adjust our target “respondents per site” upwards by the reciprocal of 0.6—that is, by 1.7. This results in:

• 2.25 sites/park

• 35 visitors/site.
  
  

Expected response rates. Based on the response rate achieved on other recent aviation-noise studies in Hawaii Volcanoes National Park, and Haleakala National Park, we expect an overall response rate of 70% or greater.^x,xi We see no reason why this will not be true, as well, for the present survey. Note that this is the acceptance rate of visitors when they are approached to take the survey. As such it is independent of the good-data rate, which applies to those actually-taken surveys.

Incremental cost adjustments. Incremental sampling costs modify these desired ratios. Our cost multipliers are: 2 for sites/backcountry park, and 5 for respondents/site—yielding:

• 2.25 sites/frontcountry park, and 5 sites/backcountry park

• 175 visitors/site.

These cost multipliers are best estimates prior to knowing the actual parks and sites that will be included. They will vary significantly from park to park and from site to site. In general, however, the extra visitor cost increment is always much less than the site and park increments. Moreover, that visitor increment is approximately the same for front and back country.

Note the cost aspect of this calculation boosts the number of sites beyond what is needed for optimum variance reduction. This site-number boost has a very important positive advantage, further justifying the boost. When these results are applied during ATMP studies, the desired prediction from the regression model will be for (1) year-long averages of a huge number of visitors, but (2) only for one site at one park (the site of that particular ATMP study). Therefore, site-average predictions from the regression are of no use. Instead, we must reduce unexplained park and site variance to an absolute minimum, to allow satisfactory one-park, one-site predictions. And boosting the number of parks and sites, based upon costs, therefore also makes sense for increased prediction certainty.

Further, NPS park managers sometimes maintain that parks/sites are “unique.” An increased sampling of parks/sites will help ensure that individual park managers recognize a park/site similar to theirs (in their judgment)—thereby helping them to accept application of the analysis results to their “unique” situation.

Resulting target sampling ratios. Table 2 contains the resulting target sampling ratios.

TABLE 2: Target sampling ratios (minimum variance, adjusted for incremental costs and good-data rate)

Site types previously measured	Park area	Corresponding site types	Target sampling ratios
			Sites per Park	Respondents per Site
Yes	Frontcountry	Overlooks Short hikes	2.5	175
No	Frontcountry	Day hikes Historical sites,
	Backcountry	Day hikes Multi-day hikes Camp sites	5	175

The target sampling ratios in Table 2 inform all the sample-size computations that follow.

Site types previously measured (first Project Purpose)

For site types previously measured (overlooks and short hikes, in frontcountry), we intend to augment the previous regressions with one or two additional acoustic metrics that are sensitive to low aircraft activity. We attempted to do this during the ongoing analysis, but were not successful in achieving our uncertainty/power goals.

For example, here is the “R” output for the most promising attempt:

Generalized linear mixed model fit by the Laplace approximation

Formula: "IntWithNQ_MorMore ~ (1|Park) + (1|Site) + 1 + SiteType + LeqAll + PEnHelos + PEnProps + PTAudTours + SiteVisitBefore + AdultsOnly + ImpNQ_VorMore + I(PEnHelos * PEnProps) + log10(PTAudTours + 0.001)"

AIC BIC logLik deviance

1488 1554 -730.9 1462

Random effects:

Groups Name Variance Std.Dev.

Site (Intercept) 0.01766 0.132891

Park (Intercept) 0.00883 0.093968

Number of obs: 1208, groups: Site, 8; Park, 4

Fixed effects:

Estimate Std. Error z value Pr(>|z|)

(Intercept) -2.574e+00 5.842e-01 -4.406 1.05e-05 ***

SiteTypeShortHike 5.830e-01 2.168e-01 2.689 0.007161 **

LeqAll 3.177e-02 8.817e-03 3.604 0.000314 ***

PEnHelos 9.758e-03 2.530e-03 3.857 0.000115 ***

PEnProps 4.280e-03 2.899e-03 1.476 0.139812

PTAudTours 7.145e-03 5.725e-03 1.248 0.212076

SiteVisitBeforeYes 5.635e-01 1.732e-01 3.253 0.001141 **

AdultsOnlyYes 4.742e-01 1.561e-01 3.037 0.002389 **

ImpNQ_VorMoreYes 2.500e-01 1.344e-01 1.860 0.062882 .

I(PEnHelos * PEnProps) 9.732e-05 9.224e-05 1.055 0.291401

log10(PTAudTours + 0.001) -7.551e-01 4.425e-01 -1.706 0.087967 .

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

In this regression, log10(PTAudTours + 0.001) is the new predictor, which has a p-value of only 0.088 in this regression. Corresponding to that is a z-value of –1.7.

To improve this regression performance, we need to scale that z-value from –1.7 to –2.8 —to obtain 95% certainty with 80% power. The required z-value ratio is 1.65 and its square equals 2.7. In turn, this squared value times the number of data points currently in the regression (1208 from the “R” output) indicates we need a total of 3260 good data points to achieve our goal. This, minus the 1208 already obtained, says we need approximately 2000 additional good points.

However, this estimate is overly pessimistic for the following reason. When we obtain additional data points for these two previously studied site types, we plan to concentrate our efforts on times of day with low aircraft activity (early morning and late afternoon), the direct opposite of the focus for all previous data collection. And for this reason, the newly acquired data points will have low values of PTAudTours, thereby contributing far more strongly to that predictor’s regression coefficient.

From our acoustical experience with noise metrics sensitive only to low-aircraft activity (such as PTAudTours), it is our conclusion that we can safely reduce the required 2000 data points to one-third that value—that is, approximately 700 additional good data points (surveyed visitors). Remember that we will add the newly collected data to existing data for future ATMP analysis. Then we must multiply this by 1.7 to account for our expected good-point rate of 60%, to yield 1200 additional respondents.

Applying this sampling target (1200 additional respondents) to the sampling ratios in Table 2, we obtain the target sample sizes in Table 3.

TABLE 3: Target sample sizes: Previously measured site types – single instrument

Park area	Site types	Target sampling sizes
		Parks	Total sites (see note 1)	Respondents per site	Total respondents (see note 2)
Frontcountry	Short hikes Overlooks	3	7	175	1,225
Note 1: Total sites split more-or-less evenly among the parks and site types. Note 2: For all three survey instruments combined, total respondents is triple this value.

This table comprises the top portion of Table 1, above.

Site types not previously measured (second Project Purpose)

For each site type not previously measured, we plan to create a new factor within the categorical predictor SiteType, and desire to measure that factor’s regression coefficient with adequate certainty and power.

For scaling, here is the relevant prior output (copied from above):

Generalized linear mixed model fit by the Laplace approximation

Formula: "Annoy_MorMore ~ (1|Park) + (1|Site) + 1 + SiteType + LeqAll + PEnHelos + PEnProps + SiteVisitBefore + AdultsOnly + I(PEnHelos * PEnProps) + ImpNQ_VorMore"

AIC BIC logLik deviance

1514 1573 -745.8 1492

Random effects:

Groups Name Variance Std.Dev.

Site (Intercept) 0.0152672 0.123560

Park (Intercept) 0.0067854 0.082374

Number of obs: 1572, groups: Site, 9; Park, 4

Fixed effects:

Estimate Std. Error z value Pr(>|z|)

(Intercept) -4.0838577 0.3667824 -11.134 < 2e-16 ***

SiteTypeShortHike 1.1275413 0.2063434 5.464 4.64e-08 ***

LeqAll 0.0158053 0.0083092 1.902 0.05715 .

PEnHelos 0.0083059 0.0026081 3.185 0.00145 **

PEnProps 0.0066900 0.0029056 2.302 0.02131 *

SiteVisitBeforeYes 0.5513902 0.1699233 3.245 0.00117 **

AdultsOnlyYes 0.1855097 0.1569553 1.182 0.23723

I(PEnHelos * PEnProps) 0.0001063 0.0000916 1.161 0.24567

ImpNQ_VorMoreYes 0.7627218 0.1481054 5.150 2.61e-07 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

In this regression, SiteType has two factors: ShortHike and Overlook (the reference factor). Because this predictor has only two factors, the difference between ShortHike and Overlook is contained entirely within the output’s regression coefficient for the non-reference factor, ShortHike. The z value for that coefficient is 5.46 (highly certain) while its “effect size” is 1.13. Therefore, the 1572 data points in this regression were able to determine a site-type “offset” between Overlook and ShortHike of 1.13, with very high certainty.

First we scale down the number of data points to just achieve our goal: 95% certainty, 80% power. The corresponding z-value goal is 2.8, which divides into 5.46 to obtain 1.95, which squares to 3.8. We therefore would have achieved our goal with only (1572)(1/3.8) = 414 data points, totaled over the 2 site types—for that effect size. That comes to 210 data points per site type.

Next we need to scale this value of 210, to account for the expected effect size of newly measured site types. The only bench mark we have to these unmeasured effect sizes is our current effect size, and we adopt this as our goal here. Therefore we need 210 good data points per site type. We multiply this by 5 for the new site types, to get 1100 additional good data points. Then multiplying by 1.7 yields a requirement of 2000 additional respondents. Finally, we multiply this by 2, to account for all the approximations in its computation—thereby yielding a sampling target of 4000 additional respondents.

We then wish to apply this sampling target (4000 additional respondents) to the sampling ratios in Table 2, above. First we divide 4000 by 175 respondents/site, to obtain 23 new sites. Then we split these 2:3 between front and backcountry, in proportion to the number of new site types in each—yielding 10 and 15 sites each, respectively. Then we use the two sites/park values in Table 4, to determine the required number of parks: 5 frontcountry and 3 backcountry. Our final sample-size targets appear in that table.

TABLE 4: Target sample sizes: New site types –single survey instrument

Park area	Site types	Target sampling sizes
		Parks	Total sites (see note 1)	Respondents per site	Total respondents
Frontcountry	Day hikes Historical sites	5	10	175	1,750
Backcountry	Day hikes Multi-day hikes Campgrounds	3	15	175	2,625
TOTAL (see note 2)					4,375
Note 1: Total sites split more-or-less evenly among the parks and site types. Note 2: For all three survey instruments combined, total respondents is triple this value.

Survey-instrument comparison (third Project Purpose)

The third project purpose is to compare results from the three survey instruments, to help determine their relative strengths and weaknesses. The quantitative measure of strength/weakness depends upon how well their results compare for the overlap survey questions.

To make that comparison, we intend to regress all three sets of responses in the manner we have described above, separately by instrument. Then we will plot the three regressions against the most important acoustic metric, along with their uncertainty bounds, to look for overlap.

Figure 1 shows such a plot from the ongoing analysis, for just one survey instrument. The main acoustic dose is plotted horizontally, while the response is plotted vertically. The small points near 0% and 100% are the underlying data, one point per visitor respondent. The solid curve is the resulting dose-response regression line.

The gray lines are a one-tenth sample of 1000 simulations of that regression (sampled from the covariance matrix of the regression coefficients, augmented by the error variances of the multilevel fixed effects). In the figure, the dashed lines encompass 95% of those 1000 simulations and hence are 95% certainty bounds on the regression.

FIGURE 1. A sample prior regression, along with its
95% confidence bounds.

Non-overlap of these particular certainty bounds is not our relevant measure, however. First we must expand them from 50% to 80% power. And second we must contract them by the square root of two, because the two sets of certainty bounds are independent from each other. Only then will their overlap or non-overlap measure sameness or not, with 95% certainty and 80% power. This we intend to do, separately for each pairing of results from the three survey instruments.

As is obvious, overlap might differ for different regions of LeqAll—that is, overlap might be a function of LeqAll. A priori we expect overlap towards the low and high ends of the LeqAll data, where data points are sparse.

Our particular question is whether we find overlap around the data centroid and therefore along the full LeqAll axis. Such overlap would show that we failed to prove a significant difference in results from the three survey instruments. In turn, that would indicate we could use a simpler instrument (actually simpler in its required acoustic-metric determination) as substitute for a more complex instrument. This will help us in our listing of trade-offs between the instruments when determining aircraft impact for the ATMPs.

Because of the complexity of the planned overlap analysis, we have not computed required sample sizes for this determination. However, we note with satisfaction the relative narrowness of our existing confidence bounds. Moreover, we will be tripling the total number of data points (from 2500 to 2500+5600) after our additional measurements—thereby narrowing these bounds further by perhaps a factor of 1.7. Will this be enough data? That depends entirely upon the “effect size” due to a change in survey instruments, and we have no estimate at all about that size.

Nevertheless, even without a computation here of required sample size, we are optimistic that we will be able to say either (1) “yes” the instruments are comparable or (2) “no” they are not—at least over some particular portion of the dose (LeqAll) range. Moreover, we are prepared to make an administrative decision about future use of these survey instruments—even if the answer to our question is “maybe”—based upon their non-mathematical strengths/weaknesses.

One additional point: We understand that we might obtain a definitive answer to this project purpose, even if we reduce the number of respondents for the second and third instrument. However, since these instruments will be administered simultaneous with the first instrument (and require the same time burden per respondent), we see no reason not to collect the same full set of data for each instrument. That is what we plan. That also satisfies the objectives of all three scientific groups on our combined research team. No one group is thereby short changed.

Unusual Sampling Procedures

Certain site types, such as remote backcountry locations, typically receive fewer visitors than other site types, such as popular scenic overlook areas. These remote locations may require more intensive survey collection (i.e., longer collection periods or multiple survey efforts at a particular location) to achieve the desired number of observations.

Data Collection Cycles

The survey protocol will include a screening question to eliminate park visitors who have previously participated in the survey from the collection. Thus, for any given park visitor, participation in the survey will be a one-time, non-recurring, event. The screening question will read as follows:

“Do you recall having taken a survey in a National Park before?” If the visitor answers “yes,” the interviewer will then ask, “Do you remember the topic of the survey?”

Visitors who remember having previously taken a survey on aviation noise will not be included in the data collection.

3. Describe methods to maximize response rates and to deal with issues of non-response. The accuracy and reliability of information collected must be shown to be adequate for intended uses. For collections based on sampling, a special justification must be provided for any collection that will not yield "reliable" data that can be generalized to the universe studied.

Response Rate and Non-response Issues

Data will be collected on-site using the attached survey instruments and trained interviewers. The presence of the interviewers should lower the incidence of item non-response in the surveys. In addition, there are observable visitor characteristics that would allow for a meaningful non-response bias analysis. These characteristics are:

• Group size

• Presence of children in the group

• Type of activity (i.e., day hiking, backpacking).

These factors have been noted for all groups in the current database, and will be noted for all future-data groups, as well—including those who choose not to participate in the survey. In turn, these factors will be used to test for non-response bias within the survey data.

Brief Summary

As discussed in Supporting Statement A, all three of the survey instruments proposed for this research effort are based on survey instruments that have been previously approved by OMB.⁵ As a result of these previous studies, there is a database of approximately 2500 visitor responses with associated direct measurements of aircraft noise exposure (all associated with the first survey instrument, however). This prior research did not yield results that could definitively be generalized and applied to the entire universe of visitors, parks, and site types—in particular to the site types newly added here. A number of salient aspects of the relationship between noise exposure and visitor response were discovered, but the limited focus on short hikes and overlooks has limited the generalizability of these relationships.

It is important to continue the research to develop an understanding of whether the context of a visitor’s park experience mediates his or her response to aircraft noise. This additional research will help to:

1. further provide an understanding of the salient aspects or combinations of aspects of the noise exposure (sound level, length of exposure, time between exposures, number of exposure events, and/or source of the noise)

2. identify additional site-specific or visitor-specific factors which may significantly influence the visitor response.

Data Sampling Regime and Reliability

Because the proposed survey collection plan includes multiple locations within each park, we are confident of achieving collections that come closer to being representative of the true range of park visitors and activities than surveys conducted at single locations. This work is part of an ongoing effort to study as many parks and sites as possible, and therefore the studies outlined herein will be incorporated into the body of existing data on response to aviation noise exposure in National Parks, further enhancing generalization.

4. Describe any tests of procedures or methods to be undertaken. Testing is encouraged as an effective means of refining collections of information to minimize burden and improve utility. Tests must be approved if they call for answers to identical questions from 10 or more respondents. A proposed test or set of tests may be submitted for approval separately or in combination with the main collection of information.

The survey instrument designs proposed for this research are based on tested, proven instruments used in previous studies of aviation noise impacts in National Parks. Therefore, we anticipate that our survey instruments will require only a modest amount of pre-testing. We plan to conduct pre-testing in National Parks and similar settings (e.g., National Historic Sites). Each pre-test will comprise fewer than 10 respondents. Pre-testing will assess question wording, question order, response-scale design and other aspects of the survey instruments. Any aspects of the instruments that are found to be unclear or confusing will be refined.

5. Provide the name and telephone number of individuals consulted on statistical aspects of the design and the name of the agency unit, contractor(s), grantee(s), or other person(s) who will actually collect and/or analyze the information for the agency.

Data collection and analysis will led by: U.S. Department of Transportation, Research and Innovative Technology Administration, John A. Volpe National Transportation Systems Center

Amanda Rapoza (617) 494-6339

Cynthia Lee (617) 494-6340

Kristin Lewis, PhD (617) 494-2130

Joshua Hassol, PhD (617) 494-3722

With consultation on statistical aspects and survey design from:

Grant Anderson, MS, Independent Consultant (978) 369-1831

James Fields, PhD, Independent Consultant (301) 439-4356

Steve Lawson, PhD, Resource Systems Group (802) 295-4999

Britton Mace, PhD, Southern Utah University (435) 865-8569

Robert Manning, PhD, University of Vermont (802) 656-3096

Peter Newman, PhD, Colorado State University (970) 491-2839

References

1 Definitions of these very technical terms—how they are measured and/or computed—can be provided upon request, or can be found in the references cited in the previous paragraph.

2 LeqAll = equivalent sound level (all aircraft), normalized to the respondent’s visit duration. This dose variable is derived from acoustic measurements taken simultaneously with the surveys, and measures sound level and duration.

3 PEnHelos and PEnProps are measures of the total sound energy from helicopters and propeller aircraft. Both are derived from acoustic measurements taken simultaneously with the surveys.

4 This predictor equals “yes” for visitors who consider Natural Quiet very important or more (paraphrased from the survey instrument).

5 OMB Nos. 1024-0088, 2120-0610, 0701-0143, 1024-0224

i Anderson, G. S., Horonjeff, R. D., Menge, C., Miller, N. P., Robert, W. E., Rossano, C., et al. (1993). Dose-Response Relationships Derived from Data Collected at Grand Canyon, Haleakala and Hawaii olcanoes National Parks. NPOA Report No. 93-6. Lexington, MA: Harris Miller Miller & Hanson.

ii Fleming, G. G., Roof, C. J., Rapoza, A. S., Read, D. R., Webster, J. C., Liebman, P. D., et al. (1998). Development of Noise Dose / Visitor Response Relationships for the National Parks Overflight Rule: Bryce Canyon National Park Study. Federal Aviation Administration. Report No. FAA-AEE-98-01. Washington, D. C.: U.S. Department of Transportation. Available from: http://www.volpe.dot.gov/acoustics/pubs1.html

iii Rapoza, A. S. (2005). Study of Visitor Response to Air Tour and Other Aircraft Noise in National Parks. Report No. DTS-34-FA65-LR1. Cambridge, MA: U.S. Department of Transportation, Volpe National Transportation Systems Center.

iv Miller, N. P., Anderson, G. S., Horonjeff, R. D., Thompson, R. H., Baumgartner, R. M., & Rathbun, P. (1999). Mitigating the Effects of Military Aircraft Overflights on Recreational Users of Parks: Final Report. Burlington, MA: Harris Miller Miller & Hanson.

v Miller, N. P. (1999). The effects of aircraft overflights on visitors to U.S. National Parks. Noise Control Engineering Journal , 47 (3), 112-117.

vi National Park Service Public Use Statistics. Available from: http://www.nature.nps.gov/stats/viewReport.cfm

vii Gelman, A. & Hill, J. (2007) Data Analysis Using Regression and Multilevel/Hierarchical Models, Cambridge University Press.

viii R Development Core Team (2008). R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0. Available from: http://www.R-project.org.

ix International Organization for Standardization, ISO (1995), Guide to the Expression of Uncertainty in Measurement, Equation E.3 (with slight change of nomenclature).

x Lawson, S. R., Hockett, K., Kiser, B., Reigner, N., Ingram, A., Howard, J., et al. (2007). Social Science Research to Inform Soundscape Management in Hawaii Volcanoes National Park: Final Report. Virginia Polytechnic Institute and State University, Department of Forestry, College of Natural Resources, Virgina. Available from: http://www.faa.gov/about/office_org/headquarters_offices/arc/programs/air_tour_management_plan/park_specific_plans/Hawaii_Volcanoes.cfm

xi Lawson, S. R., Hockett, K., Kiser, B., Reigner, N., Ingram, A., Howard, J., et al. (2007). Social Science Research to Inform Soundscape Management in Haleakala National Park: Final Report. Virginia Polytechnic Institute and State University, Department of Forestry, College of Natural Resources, Virgina. Available from: http://www.faa.gov/about/office_org/headquarters_offices/arc/programs/air_tour_management_plan/park_specific_plans/Haleakala.cfm

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