SAMPLE ALLOCATION

FOR

STRATIFIED TELEPHONE SAMPLE DESIGNS

Clyde Tucker and Robert Casady

Bureau of Labor Statistics

James Lepkowski

University of Michigan

7/17/1992
1. INTRODUCTION

One of the most difficult tasks in conducting telephone surveys is locating

households using a frame of telephone numbers. Only about twenty percent of the

telephone numbers in the United States are assigned to residences, and the search for

these residential numbers increases the costs of the survey and the length of the required

interviewing period. The most popular method for reducing the problem of locating

households was first proposed by Mitofsky (1970) and more fully developed by

Waksberg (1978). The Mitofsky-Waksberg technique capitalizes on a feature of the

distribution of working residential numbers (hereafter referred to as WRNs) in the United

States: they tend to be highly clustered within banks of consecutive numbers.

Instead of simply dialing numbers at random, Mitofsky and Waksberg outlined a

two-stage design in which banks of 100 consecutive numbers are randomly selected from

a frame constructed by appending all 10,000 four-digit suffixes to the list of area codeprefix combinations obtained from BellCore Research (BCR), and a single number from

each bank is called. If the number is residential, the rest of the numbers in the hundred

bank are retained for use in second-stage sampling. Otherwise, the bank is discarded.

By restricting calling to these screened banks, the likelihood of contacting a residence

increases threefold to about sixty percent. This procedure produces, in principle, an

unbiased sample of telephone households, and one only need know the universe of area

code-prefix combinations.

Unfortunately, there are several disadvantages which become apparent when the

Mitofsky-Waksberg technique is applied to standard, time-limited cross-sectional

surveys. They include the following:

1. The concentration of the sample within certain banks results in an intraclass 

correlation which, depending on the characteristic being measured, could 

substantially increase the variance of the estimate.

2. The k residential numbers must be contacted in each retained bank at the second 

stage. This is not usually a serious problem for hundred banks, but it would be for 

smaller bank sizes. It does mean, however, that only a portion of the numbers in a 

bank can be used before the bank is discarded.

3. Practical limits on the length of the surveying period will prevent finding the 

requisite number of households in some banks even though they exist.
4. Numbers generated as replacements for non-residential numbers in the original 

second-stage sample will receive less varied opportunities for calling, especially 

near the end of the surveying period. A small residual of numbers typically 

accumulates at the end of the study period for which a final resolution of 

residential status is impossible within the time constraints.

Several methods have been suggested for streamlining this awkward process.

Potthoff (1987) proposed a generalization of the Mitofsky-Waksberg procedure which

eliminates the need to contact k households in many of the clusters, but this technique

has its own complexities. The same is true of a method devised by Burkheimer and

Levinsohn (1988) for handling the residual numbers at the end of the survey. Brick and

Waksberg (1991) described a modification of the Mitofsky-Waksberg procedure

suggested earlier by Waksberg (1984) which eliminates the need to contact the same

number of households in every cluster. Instead, a constant number of telephone numbers

are contacted in a bank, and weights are assigned to the households found in each of

these clusters. The weight for a household is proportional to the reciprocal of the number

of households in its cluster.

Although the methodology proposed by Brick and Waksberg does simplify the

Mitofsky-Waksberg procedure, it has several problems. Only a slight bias is introduced,

but the variances can be affected more substantially. Not only will the variable weights

increase the variances (unless they are trimmed), but the cluster sizes (10 or more)

necessary to stabilize these weights may limit the number of times the banks can be

reused and exacerbate the effects of intraclass correlation.

Another way to avoid the complexity of the Mitofsky-Waksberg procedure is to

select banks of numbers based on external information. Sudman (1973) and Lepkowski

and Groves (1986) proposed sampling blocks of numbers using probabilities developed

from data on listed residential numbers. This method, however, either restricts the

sample to banks with listed numbers or requires that it be supplemented with a sample

drawn using the Mitofsky-Waksberg procedure. Furthermore, as Brick and Waksberg

observed, the listing rate in the United States is declining to the point that the number of

residential listings in a bank may not accurately reflect the total number of households.

Casady and Lepkowski (1991) offered an attractive alternative to the above designs

which also uses information on listed residential numbers. They proposed using the

counts of listed numbers in banks with one or more listed numbers to stratify the universe

of telephone numbers available from BCR into a "high- density" stratum of numbers in

banks with at least one listed number and a "low-density" stratum of all other numbers.
Estimates of the probability of contacting a residence in the high-density stratum range

from 52% when using hundred banks to 58% when using ten banks, rates comparable to

that in the second stage of the Mitofsky-Waksberg procedure. Only about 2% of the

numbers in the low-density stratum will be assigned to residences. The low-density

stratum may be discarded, sampled using an RDD procedure, or further stratified using

additional information available from BCR.

This design has several advantages over those previously discussed. Although the

information on counts of listed numbers must be purchased, first-stage screening costs

are avoided, at least for the high-density stratum. Actually, only a list of the banks with

one or more listed numbers is needed, and this probably overcomes much of the problem

associated with the declining listing rate. The counts of listed and total residential

numbers do not have to be highly correlated. Simple random sampling can be used in the

high-density stratum and, possibly, throughout. Thus, variances are not affected by

intraclass correlation, and implementation of the design is relatively straightforward.

Finally, stratifying the frame in this way leads to a number of design options.

Casady and Lepkowski discussed some of these options, and Conner and Heeringa

(1992) recently tested two designs. However, too little information on the low-density

stratum has been available until now to specify all of the alternative designs or fully

evaluate the ones that have been considered. This paper reports the results of a study

undertaken to gather the necessary information. The next section, describing the study

design, is followed by the presentation of the results. In the concluding section,

recommendations concerning alternative designs for use in a variety of situations are

offered, and future research needs are discussed.

2. THE STUDY DESIGN

In order to develop optimal designs using the Casady-Lepkowski methodology,

detailed information about the distribution of residential numbers in the low-density

stratum is needed. The first step was to obtain a file of the counts of listed residential

numbers in all of the ten banks on a frame of listed numbers kept by Donnelley

Marketing. This information, purchased in April, 1990, was merged with a file

containing the universe of ten banks developed from the BCR frame. The ten banks

without listed numbers were assigned to sampling substrata using variables previously

identified as being related to residential hit rate (Groves, Lepkowski, & Tucker, 1990).

These variables, which were obtained from the BCR file, were (1) whether the area codeexchange of the ten bank was only on the Donnelley frame, only on the BellCore frame,
or on both; (2) whether or not the ten banks in area code-exchanges appearing on the

Donnelley frame were from thousand banks with listed numbers; (3) whether or not the

area code-exchange was recently added to the frame; (4) whether the wire center in

which the area code-exchange was located contained one or more than one exchange (a

surrogate for rural-urban).

At the time of the study, late 1991, financial support could not be obtained for

collecting information on a sample of numbers from the entire frame of low density

banks, but calling could be done to augment a sampling operation in six primary

sampling units (PSUs) that had been dropped from the Consumer Price Program due to

budget reductions. These PSUs were Columbus, Ohio; Salt Lake City, Utah; Phoenix,

Arizona; Sacremento, California; a group of ten contiguous rural counties in central

Kentucky; and two neighboring counties in North Carolina which are on the border with

South Carolina. These PSUs cannot be considered representative, but they do include

both rural and urban areas. Unfortunately, the urban areas are concentrated in the West,

and the rural areas are in the South.

Table 1 gives the distributions of ten banks across the sampling strata for the six

PSUs and for the entire nation. The initial classification was based on whether or not the

ten bank contained listed residential numbers, and the banks without listed numbers (the

low-density stratum) were further subdivided as described above. The proportion of

empty banks in the six PSUs is substantially smaller than that in the national distribution.

This is to be expected given that these PSUs do not contain the vast areas in the U.S.,

particularly in the West, that are sparsely populated. Thus, the low-density substratum

most poorly represented in the study area is the one with banks in rural areas (a single

area code-exchange in the wire center) that have no residential listings in the thousand

bank. As a result, the proportion of numbers in the low-density stratum that are assigned

to residences is probably larger than in the nation as a whole.

A simple random sample of six hundred numbers were drawn from each of the five

low-density substrata represented in the six PSUs. The residential status of each number

was determined by attempting as many as twelve calls. A total of 168 numbers (5.6%)

were identified as residential. All remaining numbers in the ten banks containing these

residential numbers were called to estimate residential densities.
Table 1. Stratified distribution of ten banks for the nation and the six PSUs studied. Percentages Table 1. 

are based on total number of ten banks.

Type\Location of 10-Bank Nation Six PSUs

Total Number of 10-Banks 43,770,000 739,000

Number of Banks With Listed Numbers 14,835,887 365,870

 Donnelley Only 00.1% 00.0%

 Donnelley-BellCore 33.9% 49.5%

Number of Banks Without Listed Numbers 28,934,113 373,128

 Donnelley Only

 Empty 1000 Bank 0.4% 0.0%

 Non-Empty 1000 Bank 0.3% 0.0%

 BellCore Only

 One Prefix in Exchange

 Addition 0.1% 0.0%

 Not an Addition 0.3% 0.0%

 Two or More Prefixes in Exchange

 Addition 2.3% 0.0%

 Not an Addition 16.8% 15.3%

 Donnelley and BellCore

 One Prefix in Exchange

 Empty 1000 Bank 24.0% 2.9%

 Non-Empty 1000 Bank 4.5% 1.1%

 Two or More Prefixes in Exchange

 Empty 1000 Bank 9.8% 18.9%

 Non-Empty 1000 Bank 7.6% 12.3%

3. RESULTS

The hit rates (hi) and densities (wi) obtained from the study are given in Table 2. As

previously noted, no information was obtained in this experiment for telephone numbers

in "listed 10-banks". Hence, the information provided in Table 2 for this set of telephone

numbers is derived from general knowledge and experience obtained in previous

telephone surveys. It should also be noted that:

(1) The estimated value of h is based on a sample of 34,000 primary numbers in a

telephone survey conducted by Westat.

(2) The values of the Pi are known exactly.

(3) The zi (except for the first stratum) were determined by the equation 

z hP h i ii = .

(4) The value of z1 is derived by subtraction and h1 by h hz P 1 11 = .

(5) The wi (except for the first stratum) were estimated from an experiment 

conducted by BLS and the corresponding ti were determined by the equation 

t hw i ii = -1 ; the estimated values forw t 1 1 and are based on general knowledge.
Table 2. Approximate values of frame parameters when 10-bank characteristics are used to Table 2.

partition the combined BCR/Donnelley frame of telephone numbers. The "Residual" class

consists of those telephone numbers found in one, but not both, of the two primary frames. A

"Listed Bank" is a bank containing at least one listed number and a "Non-Empty Bank" is a bank

containing at least one Working Residential Number.

Location

 of

Telephone Number

Prop. of

Frame

Pi b g

Prop.

of

Pop.

zi b g

Hit

Rate

hi b g

Prop.

of Empty

Banks

ti b g

Hit Rate

Within

Non-Empty

Banks

wi b g

Listed 10-Bank .3390 .8865 .5736 .0440 .6000

Unlisted 10-Bank,

Unlisted 1000-bank,

1 Prefix Exchange

.2397 .0109 .0100 .9714 .3500

Unlisted 10-Bank,

Listed 1000-bank,

1 Prefix Exchange

.0450 .0191 .0930 .8371 .5710

Unlisted 10-Bank,

Unlisted 1000-bank,

2+ Prefix Exchange

.0982 .0170 .0380 .9283 .5300

Unlisted 10-Bank,

Listed 1000-bank,

2+ Prefix Exchange

.0761 .0371 .1070 .7714 .4680

Residual .2020 .0294 .0320 .8933 .3000

h t = = . . 2194 6157 and 

The "Residual" category contains all telephone numbers from unlisted 10-banks that are

found in one, and only one, of the two frames. For the six PSUs this category consisted

entirely of "BellCore only" telephone numbers.

Based on the information provided in Table 2, the frame was partitioned into the

four basic strata defined below:

 Very High Density Stratum = {All telephone numbers in a listed 10-bank}

 Moderate Density Stratum = {All telephone numbers in an unlisted 10-bank}I

{All telephone numbers in a listed 1000-bank}
 Low Density = {All telephone numbers in an unlisted 10-bank} I

{All telephone numbers in an Unlisted 1000-bank} I

{All telephone numbers in a 2+ Prefix exchange} U

 {Residual}

 Very Low Density = {All telephone numbers in an unlisted 10-bank}I

{All telephone numbers in an Unlisted 1000-bank} I

{All telephone numbers in a 1 Prefix exchange}

As can be seen in Table 3, each of the four strata comprises a significant portion of

the frame and can be clearly distinguished from the others on the basis of hit rate. Two

alternative stratification schemes were developed by collapsing the basic strata in

different ways. These alternatives are given in tables 4 and 5.

Table 3. Approximate values of the frame parameters for the Basic Stratification Scheme. Stratum

definitions are given below.

Stratum

Prop. of

Frame

( ) Pi

Prop. of

Population

( ) zi

Hit Rate

( ) hi

Prop. of Empty

10-Banks

( ) ti

Hit Rate Within

Non-Empty Banks

( ) wi

Very High

Density .3390 .8865 .5736 .0440 .6000

Moderate

Density .1211 .0562 .1018 .7958 .4985

Low

Density .3002 .0464 .0339 .9047 .3557

Very Low

Density .2397 .0109 .0100 .9714 .3500
Table 4.Approximate values of the frame parameters for the First Alternative Stratification Scheme;

the Moderate Density Stratum and Low Density Stratum have been collapsed into a single

Moderate\Low Density Stratum.

Stratum

Prop. of

Frame

( ) Pi

Prop. of

Population

( ) zi

Hit Rate

( ) hi

Prop. of Empty

10-Banks

( ) ti

Hit Rate Within

Non-empty Banks

( ) wi

Very High

Density .3390 .8865 .5736 .0440 .6000

Moderate\Low

Density .4213 .1026 .0534 .8733 .4214

Very Low

Density .2397 .0109 .0100 .9714 .3500

Table 5. Approximate values of the frame parameters for the Second Alternative Stratification

Scheme; the Low Density Stratum and the Very Low Density Stratum have been collapsed into a

single Low\Very Low Density Stratum.

Stratum

Prop. of

Frame

( ) Pi

Prop. of

Population

( ) zi

Hit Rate

( ) hi

Prop. of Empty

10-Banks

( ) ti

Hit Rate Within

Non Empty Banks

( ) wi

Very High

Density .3390 .8865 .5736 .0440 .6000

Moderate

Density .1211 .0562 .1018 .7958 .4985

Low\Very Low

Density .5399 .0573 .0233 .9343 .3546

Stratified designs based on the frame stratification given in tables 3-5, as well as the

Mitofsky-Waksberg design, were compared to simple RDD sampling of the combined

frame using the cost model described by Waksberg (1978) and used by Casady and

Lepkowski (1991). Specifically, the sample designs included in the study were

Design 1. Mitofsky-Waksberg sampling applied to combined frame. It is not 

practical to use 10-bank second stage clusters for this design so 100-bank clusters 

were assumed. The proportional reduction in variance is from Casady and 

Lepkowski (1991).

Design 2. Frame stratified as in Table 3.\ Simple RDD sampling within each of the 

four strata with stratum sample sizes determined by optimal allocation.

Design 3. Frame stratified as in Table 4.\ Simple RDD sampling within each of the 

three strata with stratum sample sizes determined by optimal allocation.
Design 4. Frame stratified as in Table 5.\ Simple RDD sampling within each of the 

three strata with stratum sample sizes determined by optimal allocation.

 The proportional reductions in variance or cost for these designs, for particular cost

ratios, are in tables 6 and 7. For small cost ratios, Mitofsky-Waksberg does slightly

better (28% vs. 26% for a cost ratio of 2), but the reverse is true for large costs ratios.

Although, the gains over simple RDD sampling are quite small for a cost ratio of 20 (1 to

3%), the efficiency of the new designs is twice that of Mitofsky-Waksberg. In the case

of the most typical cost ratios (Table 7), there are virtually no differences in efficiency

among the designs.

Table 6. Projected proportional reduction in variance\cost (relative to simple RDD sampling of the

combined frame) for four alternative sample designs. All four of the alternative designs sample

from the entire combined frame and hence cover all of the target population. Cost ratios are

those considered by Waksberg (1978).

Sample Design

Proportional Reduction in Variance or Cost Prop. of

Population

g = 2 g =10 g = 20 Not in Scope

1. Mitofsky-Waksberg .2811 .0597 .0135 .0000

2. Basic Strat. \ OA .2665 .0698 .0296 .0000

3. First Alter. \ OA .2560 .0654 .0274 .0000

4. Second Alter. \ OA .2563 .0639 .0260 .0000

Table 7. Projected proportional reduction in variance\cost (relative to simple RDD sampling of the

combined frame) for four alternative sample designs. All four of the alternative designs sample

from the entire combined frame and hence cover all of the target population. Cost ratios are

typical of research situations.

Sample Design

Proportional Reduction in Variance or Cost Prop. of

Population

g = 4 g = 6 g = 8 Not in Scope

1. Mitofsky-Waksberg .1719 .1161 .0783 .0000

2. Basic Strat. \ OA .1683 .1185 .0890 .0000

3. First Alter. \ OA .1601 .1119 .0836 .0000

4. Second Alter. \ OA .1595 .1109 .0823 .0000

The sample designs discussed above assume that the sample will be drawn from the

entire frame using optimal allocation, but, at the discretion of the researcher, part of the

frame can be discarded to further improve efficiency at the risk of some bias. Designs

using only part of the frame are referred to here as "truncated" designs; our attention will

be limited to designs that achieve truncation through the elimination of an entire stratum.

Several options are available depending on the initial stratification scheme chosen and
the amount of potential bias that can be tolerated. The Mitofsky-Waksberg design is not

considered in the following because the stratification schemes, and hence the truncation

strategies, are based on ten banks; this dictates that the Mitofsky-Waksberg design would

of necessity be applied to 10-banks which is not practical. Had the strata been

constructed from hundred banks, truncated Mitofsky-Waksberg designs could have been

evaluated.

The first three truncated designs discard the "Very Low Density" stratum as defined

in tables 3 and 4:

Design 1. Simple RDD sampling applied to the First Truncation Frame.

Design 2. First Truncation Frame stratified as in Basic Stratification Scheme and 

Simple RDD sampling within each of the three remaining strata; stratum sample 

sizes determined by optimal allocation.

Design 3. First Truncation Frame stratified as in First Alternative Stratification 

Scheme and Simple RDD sampling within each of the two remaining strata; stratum 

sample sizes determined by optimal allocation.

Results for these three designs are given in Tables 8 and 9. Just eliminating the "Very

Low Density" stratum (about a fourth of all ten banks) from a simple RDD sampling

design increases efficiency by nearly 20% for a cost ratio of 2, but the gain is almost a

third when either the basic stratification or the first alternative (Table 4) is used.

However, this is only a gain of about 5-6% over using these sampling strata with the

entire frame; and the same is true when the cost ratio is between 4 and 10. In all of these

designs, about 1% of the frame is lost. The potential bias is likely to be inconsequential,

especially when surveying the general population of telephone households.

Table 8. Projected proportional reduction in variance\cost (relative to simple RDD sampling of the

combined frame) for four alternative sample designs based on sampling from the combined

frame less the "Very Low Density" stratum. Cost ratios are those considered by Waksberg

(1978).

Sample Design

Proportional Reduction in Variance or Cost Prop. of

Population

g = 2 g =10 g = 20 Not in Scope

1. Trun1\RDD .1898 .0778 .0448 .0109

2. Trun1(Basic Strat.) \ OA .3296 .1092 .0568 .0109

3. Trun1(First Alter.) \ OA .3194 .1049 .0457 .0109
Table 9. Projected proportional reduction in variance\cost (relative to simple RDD sampling of the

combined frame) for four alternative sample designs based on sampling from the combined

frame less the "Very Low Density" stratum. Cost ratios are typical of research situations.

Sample Design

Proportional Reduction in Variance or Cost Prop. of

Population

g = 4 g = 6 g = 8 Not in Scope

1. Trun1\RDD .1359 .1102 .0912 .0109

2. Trun1(Basic Strat.) \ OA .2234 .1670 .1325 .0109

3. Trun1(First Alter.) \ OA .2153 .1606 .1272 .0109

The other two truncated sample designs, which discard the "Low/Very Low

Density" stratum (as given in Table 5), are

Design 1. Simple RDD sampling applied to the Second Truncation Frame.

Design 2. Second Truncation Frame stratified as in Second Alternative Stratification

Scheme and Simple RDD sampling within each of the two remaining strata; stratum 

sample sizes determined by optimal allocation.

Table 10. Projected proportional reduction in variance\cost (relative to simple RDD sampling of

the combined frame) for three alternative sample designs based on sampling from the combined

frame less the "Low Density" stratum. Cost ratios are those considered by Waksberg (1978).

Sample Design

Proportional Reduction in Variance or

Cost

Prop. of

Population

g = 2 g =10 g = 20 Not in Scope

1. Trun2\RDD .4198 .1722 .0990 .0573

2. Trun2(Second Alter.) \ OA .4467 .1768 .1006 .0573

Table 11. Projected proportional reduction in variance\cost (relative to simple RDD sampling of

the combined frame) for three alternative sample designs based on sampling from the combined

frame less the "Low Density" stratum. Cost ratios are typical of research situations.

Sample Design

Proportional Reduction in Variance or

Cost

Prop. of

Population

g = 4 g = 6 g = 8 Not in Scope

1. Trun2\RDD .3087 .2442 .2019 .0573

2. Trun2(Second Alter.) \ OA .3233 .2534 .2083 .0573

As can be seen in the results presented in Tables 10 and 11, almost 6% of the population

is not covered for these two designs. On the other hand, over half of all telephone

numbers have been discarded. The resulting increase in efficiency is substantial,

particularly when the cost ratios are less than ten. With this much of the frame

eliminated, stratification does not offer much of an advantage over simple RDD
sampling. The potential bias created from the loss of 6% of the telephone households

could be serious, depending on the characteristics of interest.

4. CONCLUSIONS

Even if the Mitofsky-Waksberg procedure can be easily administered or the BrickWaksberg modified design used, potential intraclass correlation can increase the variance

in estimates. This problem is eliminated with the list-assisted designs presented here;

and, furthermore, the increase in efficiency for the designs using the whole frame is

otherwise comparable to the second stage of Mitofsky-Waksberg. The truncated

designs, especially the second one, provide additional increases in efficiency if the

potential biases can be tolerated. These conclusions hold for most reasonable cost ratios.

If the cost ratio is very large, 20 or more, none of the designs, including MitofskyWaksberg, are much better than simple RDD sampling.

For sensitive situations in which it is important to demonstrate that the entire

population has been covered, the basic stratified design and the two alternatives are

comparable. In less sensitive situations where a small potential bias is acceptable, the

first truncation designs using the basic stratification scheme or the first alternative do

increase efficiency somewhat. It is the second truncation, however, which produces large

gains compared to using the whole frame, and simple RDD sampling in the reduced

frame does about as well as stratifying. The problem is that the potential bias in this case

can be large, especially if the interest is in certain subpopulations. For instance, the

portion of the frame truncated that comes from the "Residual" category has a

disproportionately large share of college housing.

The results reported here do not take into account first-stage costs. More

information about these costs is needed, and they should be incorporated in the cost

model. For the Mitofsky-Waksberg design, these are screening costs. For the listassisted designs, the Donnelley file must be purchased. In addition, all of the designs

require the BellCore file, and some programming and processing costs always will be

incurred. The processing costs for passing the Donnelley file may be quite large,

depending on the available hardware and software. Regardless of the design chosen,

costs usually can be amortized over several survey administrations.

A study which will provide the stratum hit rates at the national level will be

completed next year. As mentioned earlier, these estimates are expected to be slightly

smaller than those found in the 6 PSUs. Thus, the potential biases that result from

discarding part of the frame may be even less than reported here.
References

Brick, J.M., and Waksberg, J. (1991), "Avoiding Sequential Sampling with Random

Digit Dialing," Survey Methodology, Vol. 17, No. 1, June, pp. 27-42.

Burkheimer, G.J., and Levinsohn, J.R. (1988), "Implementing the Mitofsky--Waksberg

Sampling Design with Accelerated Sequential Replacement," in Telephone

Survey Methodology, (Eds. R.M. Groves, et al.), New York: Wiley, pp. 99-112.

Casady, R.J., and Lepkowski, J.M. (1991), "Optimal Allocation for Stratified Telephone

Survey Designs," Proceedings of the Section on Survey Research Methods,

American Statistical Association, pp. 444-447.

Conner, J.H., and Herringa, S.G. (1992), "Evaluation of Two New Cost Efficient RDD

Designs," paper presented at the annual meeting of the American Association for

Public Opinion Research, St. Petersburg, FL.

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presented at the annual meeting of the American Association for Public Opinion

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Size Design for Telephone Sampling," Proceedings of the Section on Survey

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