METHODS OF SELECTING SAMPLES IN MULTIPLE SURVEYS TO REDUCE

RESPONDENT BURDEN

Charles R. Perry, Jameson C. Burt and William C. Iwig, National Agricultural Statistics Service

Charles Perry, USDA/NASS, Room 305, 3251 Old Lee Highway, Fairfax, VA 22030

KEY WORDS: Respondent burden, multiple

surveys, stratified design

Summary

The National Agricultural Statistics Service (NASS)

surveys the United States population of farm

operators numerous times each year. The list

components of these surveys are conducted using

independent designs, each stratified differently. By

chance, NASS samples some farm operators in

multiple surveys, producing a respondent burden

concern. Two methods are proposed that reduce

this type of respondent burden. The first method

uses linear integer programming to minimize the

expected respondent burden. The second method

samples by any current sampling scheme, then,

within classes of similar farm operations, it

minimizes the number of times that NASS samples

a farm operation for several surveys.

The second method reduces the number of times

that a respondent is contacted twice or more within

a survey year by about 70 percent. The first method

will reduce this type of burden even further.

Introduction

The National Agricultural Statistics Service (NASS)

surveys the United States population of farm

operators numerous times each year. Some surveys

are conducted quarterly, others are conducted

monthly and still others are conducted annually.

Each major survey uses a list dominant multiple

frame design and an area frame component that

accounts for that part of the population not on

the list frame. The list frame components of these

surveys constitute a set of independent surveys,

each using a stratified simple random sample design

with different strata definitions. With the current

procedures some individual farm operators are

sampled for numerous surveys while other farm

operators with similar design characteristics are

hardly sampled at all. Within the list frame

component, two methods of sampling are proposed

that reduce this type of respondent burden.

Historically, NASS has attempted to reduce

respondent burden and also reduce variance. In

1979, Tortora and Crank considered sampling with

probability inversely proportional to burden. Noting

a simultaneous gain in variance with a reduction in

burden, NASS chose not to sample with probability

inversely proportional to burden. NASS has reduced

burden on the area frame component of its surveys.

There, a farmer sampled on one survey might be

exempt from another survey, or farmers not key

to that survey might be sampled less intensely.

Statistical agencies in other countries have also

approached respondent burden. For example, the

Netherlands Central Bureau of Statistics does some

co-ordinated or collocated sampling, ingeniously

conditioning samples for one survey on previous

surveys (de Ree, 1983).

Formal Description of Methods I and II

Method I is formally described by four basic tasks.

(a) Cross-classify the population by the stratifications used in the individual surveys. This

produces the coarsest stratification of the population that is a substratification of each individual stratification.

(b) Proportionally allocate each of the individual

stratified samples to the substrata. Use

random assignment between substrata where

necessary.

(c) Apply integer linear programming within each

substratum to assign the samples to the labels

of units belonging to the substratum so that

the respondent burden is minimized.

(d) Randomize the labels to the units of

substratum. The final assignment within each

substratum is a simple random sample with

respect to each of the proportionally allocated

samples.
Method II is formally described by four basic tasks.

(a) Using an equal probability of selection technique within a stratum, select independent stratified samples for each survey. Notice that the

equal probability of selection criterion permits

efficient zonal sampling techniques on each survey within strata. Currently, within strata

samples are selected systematically with records essentially in random order.

(b) Substratify the population by cross-classifying

the individual farm units according to the

stratifications used in the individual surveys.

(c) Randomly reassign within each substratum

the samples associated with units having

excess respondent burden to units having less

respondent burden.

(d) Iterate the reassignment process until it

minimizes the number of times that NASS

samples a farm operator for several surveys in

the substratum.

For both methods, define respondent burden by an

index that represents the comparative burden on

each individual sampling unit in the population.

Each survey considered is assigned a burden value.

When a sampling unit is selected for multiple

surveys, the burden index may be additive or

some other functional form dependent on the

individual survey burden values. Consequently,

each sampling configuration is assigned a unique

respondent burden index.

For any reasonable respondent burden index, the

first method minimizes the expected respondent

burden. This follows easily from the following

observations, where it is assumed that for each

of the original surveys an equal probability of

selection mechanism (epsm) is used within strata.

First, from the independence of the original sample

designs, it follows that for each individual unit the

expected burden from the original stratified samples

is equal to the expected respondent burden using

proportional allocation followed by epsm sampling

within substrata. Since the respondent burden

over any population is the sum of the respondent

burden on the individuals of the population, the

equality holds for the entire population or any

subpopulation including the substrata. That is,

the expected respondent burden over any arbitrary

substratum for the proportionally allocated samples

is equal to the expected respondent burden of

the original stratified sample allocations over the

substratum. Originally, these allocations are

random to each substratum, constrained only so

that the substratum sample sizes sum to their

stratum sample size. Second, for the first method

the respondent burden is minimized over each

substrata by the linear programming step.

Regarding variance reduction, this means that if the

original sample was selected using simple random

sampling within each stratum, then the first method

reduces respondent burden without any offsetting

increase in variance, since proportional allocation

is at least as efficient as simple random sampling.

However, the first method would be less efficient

for variance than zonal sampling unrestricted by

burden. But the second method, by reallocating

some zonal sampling units to reduce respondent

burden, may only slightly increase variance over no

reallocation and then only when zonal sampling is

effective.

A Simple Simulation of Method I

Method I reduces respondent burden in the following

simulation of two surveys. Survey I samples n = 20

from N = 110. Survey II also samples n = 20 from

N = 110, though each of its strata has either a larger

or smaller population size (N.1 = 40 and N.2 = 70)

than the corresponding strata of survey I (N1. = 30

and N2. = 80). Here, the first subscript corresponds

to the first survey, with its strata 1 and 2. Similarly, the second subscript corresponds to the second

survey. For example, N21 = 30 corresponds to the

size of the population in stratum 2 of survey I and

in stratum 1 of survey II, while  ̄n

(1)

21 = 3.75 corresponds to the proportional allocation of survey I’s

stratum 2 sample, n

(1)

2. = 10, to the population in

both stratum 2 of survey I and stratum 1 of survey

II.

Survey I Survey II

Stratum 1 Stratum 2

N11 = 10 N12 = 20 N1· = 30

Stratum 1 n ̄

(1)

11

= 3.33 n ̄

(1)

12 = 6.67 n

(1)

1·

= 10

n ̄

(2)

11

= 2.5 n ̄

(2)

12 = 2.85

N21 = 30 N22 = 50 N2· = 80

Stratum 2 n ̄

(1)

21

= 3.75 n ̄

(1)

22 = 6.25 n

(1)

2·

= 10

n ̄

(2)

21

= 7.5 n ̄

(2)

22 = 7.15

N·1 = 40 n

(2)

·1

= 10 N·2 = 70 n

(2)

·2

= 10
With two surveys, at most we will sample a

respondent twice. For the above two surveys,

without any proportional allocation, we simulated

two independent stratified simple random samples 3

million times. These simulated samples produced,

on average, 3.6 double hits for the whole population

of 110 potential respondents, and four percent of

the simulations produced 7 or more double hits.

With the proportional allocations indicated in the

diagram for Method I, the population exceeds the

total sample for both surveys in each substratum,

so no sampling unit needs to be selected for

both surveys. The high respondent burdens of

independent sampling are reduced to 0 double hits

with Method I!

Operational Description

Basic Notation

Let U = {ui}

N

i=1 be a finite population of size N.

Suppose that U is surveyed on K occasions and that

on each occasion a different independent stratified

design is used. For these K stratified designs, denote

the survey occasion by k = 1, 2, . . . K and let us use

the following notation.

H(k) :the number of strata for design k,

U

(k)

h

:the units (the set of them) in stratum h for design k,

N

(k)

h

:the size of stratum h for design k,

n

(k)

h

:the sample size in stratum h for design k,

f

(k)

h

= n

(k)

h

/N(k)

h

:the sampling fraction in stratum h for design k,

n(k) =

HP

(k)

h=1

n

(k)

h

:the overall sample size for design k, and

N = N(k) =

PH(k)

h=1

N

(k)

h

:the overall population size.

Remark

Requiring the population to be exactly the same for

each survey may seem rather restrictive. However

it is not, since, for each survey, one can easily

introduce an extra stratum that contains the units

not covered by that survey. Obviously the sample

sizes associated with the extra noncovered strata are

taken to be zero. This permits one to apply either

Method I or Method II over years.

Warning: In multiyear applications, care must be

taken to ensure that no information from the sample

data is used to update any of the frames being

considered. Failure to do so can lead to biased

estimates. These are the same restrictions that

apply to the permanent random number techniques

discussed by Ohlsson (1993).

Method I

Using this notation for Method I, we next describe a

sequence of simple data manipulation steps that can

be used operationally to perform tasks (a) through

(d) on page 1 for each of the K surveys.

Suppose that each unit, ui, of the population U has

been stratified for each of the K surveys. Further

suppose that this information has been entered into

a file containing N records, so that the ith record

contains the stratification information for unit i. To

be definitive, assume that the variable S(k) denotes

the stratum classification code for survey k and

that S(k : i) denotes the value of the stratum

classification code for unit ui.

For each survey k (k = 1, 2, . . . , K) perform the following sequence of operations.

(a) Sort the data file by the variables S(k), . . . ,

S(K), S(1), . . . , S(k − 1). This will

hierarchically arrange the records of the

population, first by the stratification of survey

k, by the stratification of survey k + 1

within the stratification of survey k, then

by the stratification of survey k + 2 within

the stratification of survey k + 1, . . . , by

the stratification of survey K within the

stratification of survey K − 1, then by

the stratification of survey 1 within the

stratification of survey K, . . . , then by

the stratification of survey k − 1 within the

stratification of survey k − 2. In terms of the

substrata formed by the cross-classification,

the records of the population are arranged

sequentially after sorting as

U

(k,k + 1,. . . ,K,1,. . . ,k − 2,k − 1)

1 , 1 ,. . . , 1 ,1,. . . , 1 , 1 ,

U

(k,k + 1,. . . ,K,1,. . . ,k − 2,k − 1)

1 , 1 ,. . . , 1 ,1,. . . , 1 , 2 ,

.

.

.

U

(k,k + 1,. . . ,K,1,. . . ,k − 2, k − 1 )

1 , 1 ,. . . , 1 ,1,. . . , 1 ,H(k-1) ,

U

(k,k + 1,. . . ,K,1,. . . ,k − 2,k − 1)

1 , 1 ,. . . , 1 ,1,. . . , 2 , 1 ,

.

.

.

U

(k , k + 1 ,. . . , K , 1 ,. . . , k − 2 , k − 1 )

H(k),H(k+1),. . . ,H(K),H(1),. . . ,H(k−2),H(k−1) − 1

,

U

(k , k + 1 ,. . . , K , 1 ,. . . , k − 2 , k − 1 )

H(k),H(k+1),. . . ,H(K),H(1),. . . ,H(k−2),H(k−1)
where

U

(k ,. . . , K , 1 ,. . . ,k − 1 )

hk,. . . ,hK,h1,. . . ,hk−1

= U

(k)

hk

T

. . . TU

(K)

hK

T

U

(1)

h1

T

. . . TU

(k−1)

hk−1

= U

(1)

h1

T

. . . TU

(k−1)

hk−1

T

U

(k)

hk

T

. . . TU

(K)

hK

= U

(1 , 2 ,. . . ,k − 1 , k ,k + 1 ,. . . , K )

h1,h2,. . . ,hk−1,hk,hk+1,. . . ,hK

Both the size and sequential arrangement of

the substrata of stratum h for survey k are

displayed schematically as

N

(k,k + 1,. . . ,K,1,. . . ,k − 2,k − 1)

h , 1 ,. . . , 1 ,1,. . . , 1 , 1

N

(k,k + 1,. . . ,K,1,. . . ,k − 2,k − 1)

h , 1 ,. . . , 1 ,1,. . . , 1 , 2

.

.

.

N

(k,k + 1 ,. . . , K , 1 ,. . . ,k − 2,k − 1)

h ,hk+1,. . . ,hK,h1,. . . , hk-2 , hk-1

.

.

.

N

(k, k + 1 ,. . . , K , 1 ,. . . , k-2 , k-1 )

h ,H(k+1),. . . ,H(K),H(1),. . . ,H(k-1)-2,H(k-1)-1

N

(k, k + 1 ,. . . , K , 1 ,. . . , k-2 , k-1 )

h ,H(k+1),. . . ,H(K),H(1),. . . ,H(k-1)-1,H(k-1)

where

N

(k ,. . . , K ,1,. . . , k − 1 )

hk,. . . ,hK,1,. . . ,Hk−1

denotes the number of units in

U

(k ,. . . , K ,1,. . . , k − 1 )

hk,. . . ,hK,1,. . . ,Hk − 1

.

(b) To randomly proportion the sample n

(k)

h

for

stratum h of survey k to the subintervals of

stratum k:

(1) Divide the length of stratum h for

survey k, N

(k)

h

, into a sequence of

n

(k)

h

subintervals of integer length that

differ in length by at most 1. Do

this by forming N

(k)

h

n

(k)

h

as yet unpopulated

subintervals, each with the length n

(k)

h

,

leaving N

(k)

h −

μ· N

(k)

h

n

(k)

h

 ̧

n

(k)

h

¶

imaginary population units to be assigned.

Randomly distribute these remaining

imaginary units (without replacement)

to the ·

N

(k)

h

n

(k)

h

 ̧

subintervals. Now

populate these subintervals by randomly

selecting a starting unit from the N

(k)

h

units. This starting unit begins the

first subinterval, with its size randomly

determined as above, ·

N

(k)

h

n

(k)

h

 ̧

or ·

N

(k)

h

n

(k)

h

 ̧

+

1. Sequentially continue to populate the

above subintervals, wrapping around to

the first unit for one of the subintervals.

This method of forming subintervals

will let us keep the same probability

of selection n

(k)

h

N

(k)

h

for each unit in that

subinterval. It does not choose a sample.

(2) Randomly select an integer from each subinterval [while this integer corresponds to

a population unit, it is not used here to

select that population unit–for that, see

(d) below].

The number of these random integers falling

in the interval corresponding to

N

(k ,k + 1 ,. . . , K , 1 ,. . . ,k − 2,k − 1)

hk,hk+1,. . . ,hK,h1,. . . , hk-2 , hk-1

in the sequential ordering is the size of the

randomly proportioned sample for survey k to

be drawn from the substratum population

U

(k ,k + 1 , . . . , K , 1 , . . . , k − 2 , k − 1 )

hk,hk+1, . . . ,hK,h1, . . . ,hk − 2,hk − 1

.

Denote this sample size for the substratum by

m

(k ,k + 1 ,. . . , K , 1 ,. . . , k − 2 , k − 1 )

hk,hk+1,. . . ,hK,h1,. . . ,hk − 2,hk − 1

or

m

(k)

h1,...,hk,hk+1,...,hK

where the subscripts in the last expression are

understood to be in natural order.

Repeating steps (a) and (b) above for

each of the K surveys, we have randomly

proportioned the K original stratified sample

sizes to the substrata.

(c) Next we describe how to use integer linear

programming to assign within a substratum

the above proportioned samples to the

substratum unit labels–not specific population

units yet. We do this so that the respondent

burden is minimized for an arbitrary positive

linear respondent burden function (index).

Suppose that m(1), m(2), . . . , m(K)samples

have been randomly proportioned to a

substratum of size M. Clearly the random

proportioning procedure described above

insures that m(k) ≤ M for k = 1, 2, . . . , K.
Moreover, if the size of the total sample m =

m(1)+m(2)+. . .+m(K)randomly proportioned

to the substratum is less than or equal to M,

then any positive linear respondent burden

index is minimized by selecting the total

sample m by simple random sampling (SRS)

without replacement (WOR) where the first

m1 units selected are associated with survey

I, the second m2 units selected are associated

with survey II, etc.

If the size of the total sample m =

m(1) + m(2) + · · · + m(K)is greater than

M, then linear integer programming can

be used to find an assignment of the

total sample to the (unspecified) labels of

the stratum that minimizes the respondent

burden. Reiterating, we are working with

labels here, so we are considering the burden

of an arbitrary unit in the substratum, not the

population units themselves, though we will

use the natural terminology “population unit.”

When assigning samples from K surveys to

the population units, there are 2K possible

ways of assigning the samples to any one

population unit. These possible assignments

can be represented by the 2K K-dimensional

vectors, call them assignment configurations,

~v1 =





0

0

0

.

.

.

0



 , ~v2 =





1

0

0

.

.

.

0



 , ~v3 =





0

1

0

.

.

.

0



 ,

.

.

.

~vK+1 =





0

0

0

0

.

.

.

1





, ~vK+2 =





1

1

0

0

.

.

.

0





, ~vK+3 =





1

0

1

0

.

.

.

0





,

.

.

.

~v

2K−1

=





0

1

1

1

.

.

.

1





, ~v

2K =





1

1

1

1

.

.

.

1





.

where component k of the vector is 1 if

the unit is sampled for the kth survey and

0 otherwise. Now we must determine the

number x1 of the population units to assign

the configuration ~v1, the number x2 to assign

the configuration ~v2, . . . , the number x2K to

assign the configuration ~v

2K .

Suppose the ith assignment configuration, represented by the ith assignment configuration

vector ~vi, produces a respondent burden of

bi ≥ 0. Then the problem of assigning the

m(1), m(2), . . . , m(K)samples to the M (unspecified) unit labels such that the total respondent burden over the substratum is minimized is equivalent to minimizing the linear

objective function (respondent burden index)

f(x1, x2, . . . , x2K )

= b1x1 + b2x2 + . . . + b

2K x2K

= ~b ~xT

subject to the K + 1 linear constraints







~v1x1 + ~v2x2 + · · · + ~v

2K x2K = ~m =

(m(1), m(2), . . . , m(K))

0 ← K constraints

x1 + x2 + · · · x2K = M ,

where x1, x2, . . . , x2K are non-negative integers.

Since ~vK+2 , . . . , ~v

2K can each be written as

a nonnegative integer combination of ~v2, . . . ,

~vK+1 and since m(k) ≤ M for each k, it is easy

to see that

~v2x2 + ~v3x3 + · · · + ~v

2K x2K

= (m(2), m(3), . . . , m(K))

0

has a solution over the nonnegative integers,

say x2, . . . , x2K . Setting

x1 = M − x2 − x3 − · · · − x2K

then provides a feasible solution to the integer

linear programming problem. So there exists

a solution and hence there exists an optimal

solution.

(d) Finally, select specific sampling units ui from

the population. Consider a specific substratum and treat other substrata similarly. From

the results of (c) above, we now randomly choose

x2 farmers from the M substratum farmers

for the configuration ~v2, randomly choose x3

farmers for the configuration ~v3, . . . , randomly

choose x2K farmers for the configuration ~v

2K .

This sample of farmers reduces burden, yet

within each stratum of each survey, this approach selects farmers with equal probability.

Note that this sample is not a type of

systematic sample–the randomness in (b)-(2)

reveals this.
Method II

In Method II, a sample is selected by some preferred

technique. That sample might be selected by

some equal probability of selection technique using

zonal sampling to reduce variance, eg, by Chromy’s

Procedure, Chromy (1981). Method II largely

retains that sample, but alters it to reduce burden.

Thus Method II alters the sample by redistributing

it within the substrata.

Since this Method II is no more complicated than

Method I and has many similarities to it, the

following description is brief.

(a) Within each stratum of each of the K surveys,

independently select a sample with equal

probability.

(b) Cross-classify the population as in (a) of

Method I. This not only cross-classifies the

population, it also cross-classifies the sample

chosen in (a) of Method II. From the

N

(k ,k + 1 ,. . . , K , 1 ,. . . ,k − 2,k − 1)

hk,hk+1,. . . ,hK,h1,. . . , hk-2 , hk-1

units in the substratum population

U

(k ,k + 1 , . . . , K , 1 , . . . , k − 2 , k − 1 )

hk,hk+1, . . . ,hK,h1, . . . ,hk − 2,hk − 1

,

denote the number sampled by

m

(k ,k + 1 ,. . . , K , 1 ,. . . , k − 2 , k − 1 )

hk,hk+1,. . . ,hK,h1,. . . ,hk − 2,hk − 1

.

This subsample size will not be changed, but

it will be distributed among the substratum’s

population in (c) below.

(c) Within a substratum, reassign or swap some

of the surveys associated with a sampling

unit having excess respondent burden to a

sampling unit have less respondent burden. If

the respondent burden index is linear, then

only one survey for one sampling unit need

be reassigned to reduce burden. For example,

when we measure respondent burden by the

number of times we hit a farmer with a survey.

Then we would move one survey from the

farmer who got 4 hits to the farmer who got

0 hits, or to the farmer who got 2 hits if no

farmer got 0 or 1 hit.

If the respondent burden is non-linear,

then sometimes more than one survey must

be reassigned to reduce burden. And

when respondent burden in non-linear, then

sometimes three sampling units (not two)

must swap to ever reduce burden.

(d) Repeat (c) above until no reassignments can

be made. Then respondent burden has been

minimized.

With this method, one might want to retain

most of the original sample selection for the

first survey but not necessarily for the other

surveys. Then, in (c), try to reassign other

surveys before reassigning the first survey.

Sequential application of Method II is justified

since each survey uses equal probability of

selection in each stratum which implies that

all units of a substratum have the same

selection probability for any given assignment

configuration.

Some NASS Examples

NASS administers many surveys with a large

number of strata. For example, the Farm Costs

and Returns Survey (FCRS/COPS) may have 18

strata, the Agriculture Survey may have 17 strata,

and the Labor Survey may have 8 strata. This

many strata over many surveys brings skepticism

to any use of Methods I or II. One would expect

many combinations of strata to contain but one

individual, even for three surveys. Methods I and

II could never reduce burden on such a sparsely

(one individual) populated combination of strata.

Fortunately, most stratum combinations are empty

while other combinations are well populated.

Indeed, not only are many substratum combinations

empty, many survey sampling combinations are

empty. In some initial testing over nine major

surveys, only 58 of the 29 = 512 possible survey

combinations occurred in Kansas and only 62 in

Arkansas based on 1991 data. This fortuitous

limitation on survey combinations gives some

optimism that many combinations of strata will be

well populated. A look at the number of population

units selected for multiple surveys provides further

optimism (see Table 1).

No burden exceeds five surveys. No sampling unit

was selected for more than five surveys, indicating

that the possible number of substrata with only one

unit is limited somewhat.

There is some optimal combination of surveys

to consider when reducing respondent burden by

either Methods I or II. More surveys result in too

few farmers being classified for any of the many

substrata combinations. Fewer surveys prevent
Table 1: Number of Survey Hits over Nine Surveys

in 1991

Arkansas Kansas

Hits Frequency Frequency

0 3491 21474

1 21125 40900

2 6136 8638

3 846 938

4 60 74

5 1 7

Methods I and II from reducing any large burdens

on some farmers; eg, when NASS surveys one farmer

for five different surveys.

In 1991, for the four major surveys – FCRS, Labor,

Quarterly AG, and Cattle/Sheep – NASS initially

sampled the following numbers of farmers.

Survey Arkansas Iowa Kansas

FCRS 666 1836 1356

Labor 576 728 440

Quarterly AG 4442 6477 5881

Cattle/Sheep 1727 5507 3204

Method II reduced burden by about 70 percent

over the three states Arkansas, Iowa and Kansas

in 1991 and 1992. Table 2 below summarizes these

reductions of burden. Since the NASS samples were

essentially random within strata, a huge reduction

can be made in burden with no cost (increase) in

variance.

Table 2: Reduction in Multiple Sample Selections

Using Method II for the FCRS, Labor, Quarterly

AG, and Cattle/Sheep Surveys

Number 1991

Selections Current Method II % Reduction

4 0 0 –

3 159 50 69

2 2620 782 70

Total 2779 832 70

Arkansas 733 205 72

Iowa 1105 252 77

Kansas 941 375 60

Number 1992

Selections Current Method II % Reduction

4 6 4 33

3 112 28 75

2 2371 749 68

Total 2489 781 69

Arkansas 735 124 83

Iowa 801 204 75

Kansas 953 453 52

Acknowledgements

The authors would like to express their appreciation

to George Hanuschak for assistance in initiating

and supporting this project early on. They would

also like to thank Ron Bosecker and Jim Davies for

continued support.

State Statistical Offices are quite concerned about

individual farmer respondent burden and want

the Agency to pursue methods to reduce it

while maintaining an acceptable level of statistical

integrity. This report is the first such statistical

attempt in recent years in the Agency. Special

thanks go to State Statisticians T. J. Byran,

Ben Klugh, Dave Frank and Howard Holden

for providing their substantial insights into the

definition and potential relief of individual farmer

respondent burden.

References

Chromy, James R. (1981). “Variance Estimators for

a Sequential Sample Selection Procedure,” Current

Topics in Survey Sampling, D. Krewski, R. Platek,

and J.N.K. Rao (Eds). Academic.

de Ree, S.J.M. (1983). A System of Co-ordinated

Sampling to Spread Response Burden of Enterprises.

Netherlands Central Bureau of Statistics.

Ohlsson, Esbj ̈orn (1993). “Coordination of

Samples Using Permanent Random Numbers,” ASA

International Conference on Establishment Survey

Proceedings.

Tortora, Robert D. and Crank, Keith N. (1978).

The Use of Unequal Probability Sampling to Reduce

Respondent Burden. USDA/National Agricultural

Research Service.