REDC ss 080910 Part B, sampling procedure and references._revpdf

SUPPORTING STATEMENT
REGIONAL ECONOMIC DATA COLLECTION PROGRAM
FOR SOUTHEAST ALASKA
OMB CONTROL NO. 0648-XXXX

B. COLLECTIONS OF INFORMATION EMPLOYING STATISTICAL METHODS
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 governmental units, households, or persons) in the
universe and the corresponding sample are to be provided in tabular form. The tabulation
must also include expected response rates for the collection as a whole. If the collection has
been conducted before, provide the actual response rate achieved.
For the vessel surveys, information in the AKFIN database for Year 2008 was used to determine
survey population characteristics. Year 2009 data should be available once the survey is
complete. The questions to be asked of survey participants will be for Year 2009 activity. The
overall population will consist of all fishing vessels making deliveries to a port in SE Alaska. In
2008, there were 2,271 such vessels. This population consists of six vessel classes as shown in
Table 1. An unequal probability sampling (UPS) procedure is used to determine the sample sizes
needed for each vessel class. UPS procedures are described in Attachment A.
The expected response rates for the vessel surveys are based on consideration of the following
factors. A previous data collection project conducted for SE Alaska (Hartman 2002) achieved an
overall response rate of about 30%. That study contained a larger number of questions including
sensitive ones. The AFSC has completed a survey similar to the proposed one for the Southwest
Alaska region and the Gulf Alaska region. The average response rates were about 20% for the
harvest sector survey. Based on these two survey programs, it is assumed that, overall, the
response rate for mail survey of fishermen for the present project will be about 25%. For a more
detailed description of the methods we will use to increase the response rate, see Item #3 below.
2. Describe the procedures for the collection, including: the statistical methodology for
stratification and sample selection; the estimation procedure; the degree of accuracy
needed for the purpose described in the justification; any unusual problems requiring
specialized sampling procedures; and any use of periodic (less frequent than annual) data
collection cycles to reduce burden.
Since the majority of gross revenue within each harvesting sector comes from a small number of
vessels, a simple random sampling (SRS) of vessels would only include a small portion of the
total ex-vessel value, and therefore, would be misleading. As a result, for this project an unequal
probability sampling (UPS) method without replacement is used to account for the unequal
distribution of harvest in each target population. The objective of the sampling task is to
estimate the employment, labor income and other input cost information for each of six
disaggregated harvesting sectors using as an auxiliary variable, ex-vessel revenues provided by
AKFIN and the Pacfic Fisheries Information Network (PacFIN) databases. Since each sector
1

will be used as a separate economic sector in an economic model, we face six separate problems
for six different sectors in sampling. For each sector, we use a UPS without replacement method
to identify sampling units. Details of the sampling methodology are described in Attachment A.
3. Describe the methods used to maximize response rates and to deal with non-response.
The accuracy and reliability of the information collected must be shown to be adequate for
the intended uses. For collections based on sampling, a special justification must be
provided if they will not yield "reliable" data that can be generalized to the universe studied.
(a) Maximizing Response Rates
Previous applications of voluntary commercial fishing surveys in Alaska (e.g., Hartman 2002)
tended to be hampered by relatively low response rates that principally resulted from the use of
long and complicated survey instruments. Commercial fishermen are frequently asked, and often
required, to participate in surveys from numerous organizations including NOAA, Alaska
Department of Fish and Game (ADF&G), and universities. As a result, commercial fishermen
are less likely to complete voluntary surveys that are lengthy, poorly-designed, or do not clearly
involve issues that are important to them. In this data collection effort, significant efforts were
made to ensure the survey instruments were short in length, contained well-designed questions,
and clearly conveyed the relationship of the data collection to issues that are important to
commercial fishermen.
The mail survey is short (i.e., six questions spanning five pages) and avoids many of the more
sensitive questions included in previously-fielded commercial fishing surveys. The set of
questions was limited to only those that are essential for achieving the objectives of the project as
outlined in Part A, Question 1. Compared with the Hartman (2002) SE Alaska commercial
fishing survey, which achieved an overall response rate of about 30%, a much smaller number of
questions will be asked. Questions on vessel expenditures are often included in surveys of
commercial fishermen. In the effort proposed here, information on simple expenditure shares
rather than actual expenditures is solicited to avoid the added complexity and likely sensitivity of
requesting this type of information. It is not necessary to ask total vessel harvest revenues
because that information is already known from the AKFIN and PacFIN databases.
The personal interviews with vessel owners, and key informant local supplier businesses and
seafood processors, will be structured with similar objectives in mind. The interviews are
designed to follow up on vessel cost information; acquire information on value added by seafood
processors, and gather information on local expenditures for labor and non-labor inputs by
supplier businesses. Information on non-labor costs will be grouped into categories, e.g., fuel,
maintenance, packaging, transportation, etc. A worksheet containing estimates of expenditures
for items in these categories as a share of total business expenditures will be used to guide the
interviews. The worksheet will be prepared using income statements taken from an earlier
economic fishing industry model. The expenditure shares in these statements will serve as
reasonable starting points, but scrutiny by the key informants will be needed to judge whether
these are valid, or if not, to update them. Questions about total business sales and expenditures of
seafood processors do not need to be asked because these can be calculated by knowing the
amounts purchased from harvesters (from AKFIN and PacFIN) and information collected about
2

value added in the manufacturing process. Omitting asking sensitive questions about actual
dollars combined with the pre-coded worksheet approach will minimize respondents’ time
burden.
To overcome concerns about confidentiality, a detailed confidentiality statement will be
distributed with the mail survey. Protection of confidentiality will also be stressed up front in the
key informant interviews. A similar confidentiality statement will be included in the advance
and transmittal letters accompanying the mail survey.
Another reason believed to have caused low response rates in previous surveys is disinterest
among respondents toward the survey purpose. Surveys collecting information that will clearly
benefit or interest respondents are more likely to be completed. The importance and benefits of
this data collection project to the respondents (fishermen, local supplier businesses, and seafood
processors) will be emphasized in the mail-outs and during interviews. This will clearly state
that with their help, the important role of the respondents' fishing and business activities in the
regional economy can be better understood. The information they provide will be used to
enhance the fishery management practices of NOAA fisheries, and thereby, increase the long-run
economic benefits to the fishermen and local businesses. Making a clear link between the
survey, their participation, the fishery and the regional economy is expected to help increase the
response rate compared with previous efforts.
In addition to the above steps taken to maximize response rates, the survey instruments (mail and
telephone) were reviewed by several researchers with expertise in Alaska fisheries and economic
surveys to ensure the quality of the materials.
A set of survey protocols to be followed was designed to maximize response rates. For the mailout survey, a modified Dillman (2000) approach will be employed that includes:
•
•
•

An advance letter notifying the respondents a few days before they receive the survey
questionnaire. This will be the first contact with the respondent.
An initial mailing sent a few days after the advance letter. Each mailing will contain
a cover letter, personalized questionnaire, and a pre-addressed stamped return
envelope.
A postcard follow-up reminder mailed 10 days following the initial mailing.

The proposed option for vessel owners to fill out a confidential and personalized web-based
questionnaire hosted on a secure internet website will make responding easier for some survey
participants. It is expected that this feature will also help to increase the response rate.
The result of the efforts described above are compact and high-quality survey instruments that
contain questions vessel owners, local businesses, and seafood processors can answer with
minimal effort. As a result, the expected response rate for the mail survey of vessel owners is
modestly expected to be approximately 25%. Through recruitment efforts to secure candidate
key informants, up to 50 personal interviews with vessel owners, processors and suppliers will
also be completed.
(b) Non-response
3

A follow-up phone call will be made to a portion of mail-out non-responders in order to
determine degree of non-response bias. The interviewer will encourage a mail response, but
provide an option for the information to be provided during the phone call. If the respondent
agrees, the mail survey will be completed over the phone. 1 Up to three attempts will be made to
contact a non-responder for the telephone interview. Individuals needing an additional copy of
the survey will be sent one with a cover letter and return envelope.
To better understand the differences between responders and non-responders, additional
comparisons will be drawn with respect to several observable characteristics: (1) geographical
area of landed fish, (2) ex-vessel value, and (3) species caught. This information is available
from AKFIN and PacFIN data for each vessel. If significant and systematic differences between
responder and non-responder groups are discovered, population parameter estimates may be
adjusted using weights derived from this information.
4. Describe any tests of procedures or methods to be undertaken. Tests are encouraged as
effective means to refine collections, but if ten or more test respondents are involved, OMB
must give prior approval.
There are no plans to conduct a pilot survey or other tests involving more than ten respondents.
5. Provide the name and telephone number of individuals consulted on the 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.
John Slanta (Census Bureau) assisted in the development and review of sampling procedures for
this project. Mr. Slanta’s contact information is (301) 763-4773.
Several NMFS economists with experience in economic survey design and implementation
reviewed the survey materials and survey protocols, including Dr. Dan Lew, Dr. Ron Felthoven,
and Dr. Brian Garber-Yonts.
Dr. Chang Seung (Alaska Fisheries Science Center) is the AFSC contact who is responsible for
project management and will participate in the development of regional economic models using
the information from this project. Dr. Seung's contact information is (206) 526-4250,
[email protected].
The contractor coordinating the project and preparing documentation is Edward Waters,
Beaverton, Oregon. Mr. Waters’s contact information is (503) 804-8857,
[email protected].

1

In this case, the harvest values for the vessel will be provided to the vessel owners so that they will not need to access their records. Having this
information on hand should greatly simplify responses for labor payments and expenditure shares. In doing this, we will make sure that the
person we will be interviewing on the phone is the true owner of the vessel so as not to breach confidentiality by providing sensitive information
to an unauthorized person. The harvest value information will not be provided to the respondent in the mail survey, as can be seen in the example
mail survey questionnaire in Attachment B.

4

The contractor performing and tabulating the survey is Shannon Davis, The Research Group,
Corvallis, Oregon. Ms. Davis’s contact information is (541) 758-1432,
[email protected].

5

ATTACHMENT A. SAMPLING PROCEDURES FOR HARVESTING SECTORS1
The objective of the vessel-level data collection proposed under this project is to estimate
employment, payments to labor, and payments for non-labor inputs for each of six disaggregated
harvesting vessel sectors using data to be collected via a mail survey. Using ex-vessel revenue
information, an unequal probability sampling (UPS) procedure will be employed to determine
the sampling plan for each of the six harvesting sectors. The UPS procedure is described below.
An expanded version of this attachment will be published in an academic journal (Seung 2010).
The literature contains many methods for conducting UPS without replacement (see, for
example, Brewer and Hanif 1983; Sarndal 1992). One critical weakness with most of these
methods is that the variance estimation is very difficult because the structure of the 2nd order
inclusion probabilities (πij)2 is complicated. One method that overcomes this problem is Poisson
sampling. However, Poisson sampling has the weakness that the sample size is a random
variable, which increases the variability of the estimates produced. An alternative method that is
similar to Poisson sampling but overcomes this weakness is Pareto sampling (Rosen 1997)3
which yields a fixed sample size.
In this project, there are two main tasks involved in estimating the harvesting vessel population
parameters using UPS without replacement. First, the optimal sample size needs to be
determined. Second, once the optimal sample size is determined, the population parameters and
confidence intervals need to be estimated. For the first task, we will use the variance of HorvitzThompson (HT) estimator from Poisson sampling in Part I below.4 For the second task, we will
use the Pareto sampling method described in Part II below (Slanta 2006). In determining the
optimal sample size in Part I, we will use information on an auxiliary variable (ex-vessel
revenue). To estimate the population parameters in Part II, we use actual response sample
information on the variables of interest (employment and labor income).
Part I: Estimating Sample Size
Step 1: Estimation of Optimal Sample Size (n*)
(A) Obtaining Initial Probabilities
To obtain the initial values of the inclusion probabilities (πi) for unit i in the population, we
multiply the auxiliary value of unit i (Xi, i.e., the ex-vessel value of vessel i in the population) by
a proportionality constant (t)5:

π = tX
i

(1)

i

where πi
Xi

: probability of vessel i being included in the survey sample
: value of the auxiliary variable (ex-vessel value of vessel i in the
population)

6

Here, t is given by
N

t=

∑X

i

i

(2)

N

∑X

V +

2
i

i

where N
V

: population size
: desired variance (of HT estimator of the population total); Poisson
variance. Here, V is given as:
2
 εX 

V =

z
1
(
/
2
)
−
α


where ε is the error allowed by the investigator [e.g., if ε is 0.1, then 10% error of
true population total ( X =

N

∑X
i =1

i

) is allowed]; and z is percentile of the standard

normal distribution. Therefore, choosing a desired variance V is equivalent to
N
(1 − π i ) X i2
setting the values of ε and z. The value of V calculated using V = ∑
πi
i =1
(Poisson variance; Brewer and Hanif 1983, page 82) with πi's being the final
values of N inclusion probabilities obtained from Step 1, will be equal to the
desired variance given at the beginning of Step 1.
Some of the resulting πi's could be larger than one. The number of certainty units (i.e., the
number of units for which πi >1) is denoted C1. If πi > 1, then we force this inclusion probability
to equal one (πi = 1).
(B) Iterations and Determination of Optimal Sample Size
We recalculate t using the noncertainty units (i.e., the units for which πi <1) obtained in (A)
above, i.e.,
M1

t=

∑X

i

i

V +

(2')

M1

∑X

2
i

i

where M1

: number of noncertainty units from (A), where M1 = N – C1.

Using equation (1) above, we calculate the inclusion probabilities for the noncertainty units by
multiplying the t value [from equation (2')] by the ex-vessel values of the noncertainty units. If
the resulting πi's are larger than one, we force them to equal one. The resulting numbers of
certainty and noncertainty units are denoted C2 ( = C1 + additional number of certainty units) and
M2 ( = M1 – additional number of certainty units), respectively, where C2 + M2 = N. Next, for
7

M2 units of noncertainty, we calculate the t and πi's again. This is an iterative process. We
continue this process until the noncertainty population stabilizes (i.e., until there is no additional
certainty unit).
If the noncertainty population stabilizes after kth iteration, there will be Ck units of certainty units
and Mk units of noncertainty units and Ck+ Mk = N. Summing over the probabilities for all these
certainty and noncertainty units, we obtain the optimal sample size (n*) as:
n* =

N

∑π

(3)

i

i

At this stage the optimal sample size may not be an integer number. In this stage, we also
compute the optimal sample size under simple random sampling (SRS)6, nsrs, and compare it
with n*.
Step 2: Determining Number of Mailout Surveys
(A) Adjustment of Probabilities
Once the optimal sample size (n*) is determined in Step 1, we divide the sample size (n*) by the
expected response rate (obtained from previous studies) to determine the number of surveys that
need to be mailed out to achieve n*. The number thus derived is denoted na (this number may
not still be an integer value). We next adjust the inclusion probabilities for the Mk noncertainty
units obtained in Step 1 above as:


 π 
π i = (na − C k )  M k i 


 ∑π i 
 i


(4)

If the resulting probabilities are larger than one (πi > 1), we make them certainties (πi = 1). The
resulting numbers of certainty and noncertainty units are denoted Ck+1 and Mk+1, respectively.
Next, we adjust the probabilities of the new set of noncertainty units (Mk+1) in a similar way
using equation (4') below:


 π 
(4')
π i = (na − C k +1 )  M k +1i 


 ∑π i 
 i

We continue this process until the noncertainty population stabilizes. The resulting numbers of
certainty and noncertainty units are Cq and Mq, respectively.

8

(B) Apply Minimum Probability Rule
At this point, we impose a minimum probability rule. UPS can have excessively large weights
(= 1/πi) and if they report a large value, then the population estimate and its variance would be
very large. In order to avoid this problem, we can impose a minimum value of the inclusion
probabilities. If m is the minimum imposed probability, then we do the following:
If πi < m, then set πi = m for each i, where i = 1, ..., N.
The value for m here is determined arbitrarily. The only cost involved in using this rule is a
small increase in sample size.7
(C) Finding an Integer Value for Sample Size
Next, we add up all the resulting inclusion probabilities. The resulting sum is denoted nb ( > na),
which may not be an integer value. Next, we adjust again the probabilities for noncertainty units
including the units for which the minimum probabilities were imposed as:



π 
π i = ( nc − C q )  M q i 


 ∑π i 

 i

(5)

where nc is the smallest integer value larger than nb (e.g., if nb = 15.3, then nc = 16). Finally, we
add up the resulting (certainty and noncertainty) probabilities. The sum of all these probabilities
is the final survey sample size (i.e., the number of surveys to be sent out to), and is denoted nm (=
nc).
Part II: Estimation of Population Parameters and Confidence Intervals
Step 3: Implementation of Pareto Sampling
After the mailout sample size (nm) for each sector is determined in Step 2, the mailout sample is
selected from each sector's population using Pareto sampling. The probability of each unit
(vessel) being in the sample in a given sector is proportional to the unit's (vessel's) ex-vessel
revenue. Because the majority of gross revenue within each sector comes from a small number
of vessels, a random sample of vessels would only include a small portion of the total ex-vessel
values.
According to Brewer and Hanif (1983), there are fifty different approaches that are used for
UPS. Most of these approaches suffer from the weakness that it is very hard to estimate the
variance. Poisson sampling overcomes this problem, and is relatively easy to implement.
However, the limitation of Poisson sampling is that the sample size is a random variable.
Therefore, in this project, we will use Pareto sampling (Rosen 1997 and Saavedra 1995) which
overcomes the limitation of Poisson sampling. The mailout sample size will be nm as determined

9

in Step 2 (C) above. We will use the inclusion probabilities obtained from Equation (5) above in
implementing Pareto sampling.
The procedure of this sampling method (Block and Crowe 2001) is briefly described here:
1.
2.
3.
4.

Determine the probability of selection (πi) for each unit i as in Equation (5) above.
Generate a Uniform (0,1) random variable Ui for each unit i
Calculate Qi = Ui (1 – πi ) / [πi (1 - Ui )]
Sort units in ascending order by Qi, and select nm smallest ones in sample.

From the above, it is clear that we will have a fixed sample size with Pareto sampling.
Step 4: Mailing out Surveys and Obtaining Actual Response Sample
Next, we will send out the surveys to the nm units (vessel owners). Actual response sample will
be obtained and the size of the actual response sample is denoted r.
Step 5: Estimation of Population Parameters (Population Total)
Using the information in the actual response sample, we calculate population parameters for
variables of interest (employment and labor income in our project), not for ex-vessel revenue,
using HT estimator (Horvitz and Thompson 1952). We are interested in estimating the
population totals (not population means) of the variables of interest. The HT estimator is given
as:
r

YöHT = ∑ wi y i

(6)

i =1

where r
wi
yi

: number of respondents
: weight for ith unit ( = 1/πi ). Note that the weights are calculated here
using the information on the auxiliary variable, not that on the variables
of interest
response
sample data of ith unit (employment or labor income)
:

However, the HT estimator needs to be adjusted for non-response. The estimator is adjusted in
the following way.
 N
 ∑Xj
 j =1
Yö =  r
 ∑ wi X i
 i =1



ö
 YHT



(7)

10

where N
Xi

: population size
: auxiliary variable of ith unit (respondents only)

Usually, we apply this adjustment to the certainties separately from the noncertainties, and then
add the two together to get a final estimate. If there are no respondents within any of the two
groups of certainty units and noncertainty units, then we collapse the two groups before applying
the adjustment. Specifically, the final estimate of population total is given by:

 N1
 ∑Xj
 j =1
ö
Y =  r1
 ∑ wi X i
 i =1


 N2

 ∑Xj
 r
 j =1
 1
 ∑ wi y i +  r2
 ∑ wi X i
 i =1
 i =1





 r
 2
 ∑ wi y i
 i =1



(8)

where N1
: number of certainty units in the population
: number of noncertainty units in the population
N2
r1
: number of respondents from certainty units
r2
: number of respondents from noncertainty units, and
N1 + N2 = N and r1 + r2 = r.
Step 6: Estimation of Variance for YöHT and Yö
Here we will calculate the variances of the population estimates for the variables of interest. The
variance estimate for Pareto sampling is given in Rosen (1997, Equation (4-11), p. 173) as:



n
m
Var (YöHT ) =

nm − 1 



 nm
y
∑ (1 − π i ) i
 i =1
πi





2


 −


 nm  1 − π i
∑ y i 
 i =1  π i
nm

∑ (1 − π
i =1

i

)





2









(9)

Since we have adjusted for nonresponse, we need to incorporate the variability due to
nonresponse into the variance. If we assume that the response mechanism is fixed 8, then we
have a ratio estimator and its variance can be found in Hansen, Hurwitz, and Madow (1953, page
514). This variance is a Taylor expansion, and is given as:

 σö2 (A) σö2 (B ) 2 COV (A, B )

Var Yö = Yö2 
+
−
2
AB
B2
 A


()

(10)

where
r

A = ∑ wi y i
i =1

11

r

B = ∑ wi X i
i =1

2

 r
 

∑ (1 − π i )(wi y i ) 
n m  r
2
 i =1
 
2
σö (A) =
∑ (1 − π i )(wi y i )  −

nm
n m − 1  i = 1

(1 − π i ) 
∑

i =1


2

 r
 

∑ (1 − π i )(wi X i ) 
r



n
i =1
 
σö2 (B ) = m ∑ (1 − π i )(wi X i )2  − 

nm
nm − 1  i = 1


(
)
1−πi
∑


i =1





 r
 r
(
)(
)
1
π
w
y
−
 r
∑
i
i i  ∑ (1 − π i )(wi X i ) 

n 
i =1
 .
  i =1
COV (A, B ) = m ∑ (1 − π i )wi2 y i X i  − 

nm
n m − 1  i = 1


(
)
−
1
π
∑
i


i =1


Step 7: Calculation of Confidence Intervals
Confidence intervals are calculated using response sample statistics obtained in steps 5 and 6.
We only choose one sample, but if there were many independent samples chosen then we would
expect on average that approximately 100(1-α) % of the confidence intervals constructed in the
following manner will contain the truth.
 Yˆ − z
Var (Yˆ ) , Yˆ + z
Var (Yˆ ) 
α /2
α /2


where Yö

(11)

: Estimated population total for employment or labor income.

Note that it is possible to use t-statistics if the sample size is small.

12

Footnotes
1. In the process of developing this document, several experts in UPS sampling assisted me
by providing helpful comments and inputs. The experts include John Slanta (U.S. Census
Bureau), Bengt Rosen (Uppsala University), Pedro Saavedra (ORC Macro), Holmberg
Anders (Statistics Sweden), Paolo Righi (ISTAT, Italy), and Bob Fay (U.S. Census). In
particular, I would like to thank John Slanta very much for his time and effort in
providing valuable inputs and advice. His suggestions and comments contributed
significantly to the development of the sampling procedures in this document. Many
thanks go to Dan Lew (NMFS) for his rigorous review and valuable suggestions which
contributed in a significant way to the improvement of this document. I also benefited
from discussions of UPS with Norma Sands at NWFSC and from the Excel file that she
developed.
2. 2nd order inclusion probability (πij) is defined as the joint probability of including in
sample the ith and jth population units.
3. Saavedra (1995) independently developed the same sampling methodology as Rosen
(1997), which he called Odds Ratio Sequential Poisson Sampling (ORSPS).
4. Although we do not use Poisson sampling itself, we do use the Poisson variance of HT
estimator of the population total.
5. Equation (1) is derived as follows.

X
HT estimator, XöHT = ∑ i , has variance,
i

2

N

πi

N

2

N

X
X
V ( XöHT ) = ∑ i (1 − π i ) = ∑ i − ∑ X i2 (Brewer and Hanif 1983, page 82)

πi
i =1 π i
For an expected sample size n,
i =1

(A)

i =1





Xi 

πi = n N


 ∑ Xi 

 i =1
Substituting (B) into (A) and solving for n,

(B)

2

N
 N

 ö

V ( X HT ) + ∑ X i2 
n =  ∑ X i 


i =1
 i =1 


Substituting (C) into (B),

(C)

13

N


Xi
∑


i =1
 X i , i = 1, 2, ... , N,
πi =
N
 ö
2 
V ( X HT ) + ∑ X i 
i =1



(D)

where V ( XöHT ) is the desired variance.
6. The optimal sample size under SRS is determined using the following standard formula:
n srs ≥

z 2 N (CV p ) 2
z 2 (CV p ) 2 + ( N − 1) ε 2

where nsrs
CVp

(Levy and Lemeshow, formula (3.14) on page 74)

: optimal sample size under SRS
: coefficient of variation of the population parameter. Since the
information on the population parameters (i.e., employment and
labor income) is not available, we use ex-vessel revenue, for
which the population information is available from CFEC.
Therefore, CVp is defined as standard deviation of the ex-vessel
revenue in the population divided by the mean.

7. This minimum probability rule is used, for example, in the Manufacturing and
Construction Division of the Census Bureau. To date, there has not been any research on
the minimum probability in the sampling literature. It is an arbitrary value and in
applications has sometimes varied between strata in the same survey. Some researchers
determine the minimum probability such that the resulting weight, which is the reciprocal
of the minimum probability, is less than or equal to the population size. Generally
speaking, this minimum probability rule has little effect on the sample size.
8. Fixed response mechanism means that a unit included in a sample is always a respondent
or non-respondent no matter what sample the unit is included in. In other words, the
probability of the unit being a respondent is either one or zero but nothing in-between.

14

References
Block, C. and Crowe, S. (2001). Pareto-πps Sampling. Unpublished Document. Statistics
Canada.
Brewer, K. and Hanif, M. (1983). Sampling with Unequal Probabilities. Springer Verlag, New
York.
Hansen, Hurwitz, and Madow (1953). Sampling Survey Methods and Theory. Volume 1.
Methods and Applications.
Horvitz, D. and Thompson, D. (1952). A Generalization of Sampling without replacement from
a Finite Universe. Journal of American Statistical Association Vol. 47, pp. 663-685.
Levy, P. and Lemeshow, S. (1999). Sampling of Populations – Methods and Applications.
Third Edition. Wiley and Sons.
Rosén, B. (1997). On Sampling with Probability Proportional to Size. Journal of Statistical
Planning and Inference, 62, 159-191.
Särndal, C.-E., Swensson, B. & Wretman, J. (1992). Model Assisted Survey Sampling. Springer
Verlag, New York.
Saavedra, P. 1995. Fixed Sample Size PPS Approximations with a Permanent Random
Number. Joint Statistical Meetings, American Statistical Association, Orlando, Florida.
Seung, C. (2010). Estimating economic information for fisheries using unequal probability
sampling. Fisheries Research. In Press.
Slanta, J. (2006). Personal Communication.

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