Discussion: Applications of Sampling 

Michael P. Cohen 

Senior Consultant to NORC 

1801 Pennsylvania Avenue NW 

Washington DC 20006-3608 

MPCohen@Juno.com

Introduction

 The three presentations in this session illustrate the diversity in the ways sampling can be applied. All three of 

them introduce interesting new ideas rather than just refining conventional approaches. 

 I shall simply discuss the papers one by one in the order presented. 

“Evolutionary Algorithms for Optimal Sample Design” by Charles Day

 This paper employs an algorithm, called the cooperative coevolutionary algorithm (CCEA), with a strong 

intuitive appeal. Let me first summarize Day’s CCEA in terms of what needs to be given in advance and what is

produced. 

Given in advance: 

Measure of size (e.g. Adjusted Gross Income) 

Number of strata H 

Simple random sampling within a stratum 

Maximum Coefficient of Variation (CV) for each of several pre-specified variables 

Produced by algorithm: 

Stratum boundaries 

Allocations (stratum sample sizes) 

 For comparison purposes, we now give the corresponding information for the well-known algorithm of Lavallée 

and Hidiroglou (1988). 

Given in advance: 

Measure of size 

Number of strata H 

Simple random sampling within a stratum 

Maximum CV for a single pre-specified variable 

Produced by algorithm: 

Stratum boundaries 

Allocations (stratum sample sizes) 

 Let’s also compare with the recent and quite different method of Gunning and Horgan (2004). 

Given in advance: 

Measure of size and number of strata H 

Simple random sampling within a stratum 

Maximum CV for a single pre-specified variable 

Simple method but positive skew in population required 

Produced by algorithm: 
Stratum boundaries 

Allocations (stratum sample sizes) 

 The Gunning and Horgan algorithm is unusual in actually requiring positive skewness in order to function 

correctly. But when there is positive skewness, it is particularly simple relative to other methods. 

 In comparing CCEA to the others, one sees that it is the only one that can control the CVs for several prespecified variables at a time, a clear advantage. The intuitive appeal of the heuristic algorithm is another 

advantage. 

 I will close this section with two questions, possibly entailing additional research: 

(1) Can number of strata H be allowed to vary (subject to a penalty)? 

(2) Can we allow probability proportional to size (pps) sampling within strata? 

“Derivation of Sample Size Formula for Cluster Randomized Trials with Binary Responses Using a General 

Continuity Correction Factor and Identification of Optimal Settings for Small Event Rates” by Majnu John 

and Madhu Mazumdar 

 

 This paper treats cluster randomized trials (CRTs). I was struck by the similarity of the issues and techniques 

with those used in survey sampling. In some cases the terminology is slightly different, but not difficult for a survey 

sampler to figure out. The unifying theme is the intraclass correlation that arises from clustering. 

 The aim of this research is determine the sample size, by which is meant the number of clusters, needed to 

guarantee no more than specified type I and II errors in doing a hypothesis test in doing a hypothesis test of the 

difference of two proportions. The authors develop a new formula for determining the sample size, (assuming equal 

sample size per cluster, an assumption made for tractability) and demonstrate its effectiveness. The example 

applications are very interesting in their own right. 

 We summarize the method in terms of what needs to be given in advance and what is produced: 

Given in advance: 

Binary outcomes 

Population means, type I error (alpha), power (one minus type II error)

Design effects (variance inflation factors, VIFs) 

Continuity correction factor c 

Sample size per cluster (same for each cluster) 

Produced by program:

Sample size (number of clusters) K 

 The program is implemented in R code that the authors supply. I tried it and it works. Supplying the code 

makes it much more likely that practitioners will use it. 

Here are two questions to close the section: 

(1) Why not use the “exact” method? (The authors, as I understand it, are working on this.) 

(2) Can the equal-sized cluster assumption be relaxed? 

“Sampling from Discrete Distributions: Application to an Editing Problem” by Lawrence Cox and Marco 

Better 

 This paper studies 2 by 2 contingency tables with count data missing for some cells but with marginal totals. It 

studies this problem with an eye toward more complex tables. We summarize the situation thusly: 

Given in advance: 

Counts of responses by category and nonresponses to two questions 

Produced by algorithm: 

Allocations of the non-responses that satisfy marginal constraints 

Method that “scales up” to higher dimensions 

 Raking is one method that one might think of to tackle this problem. As the authors note, “...ratio adjustment 

and raking are ineffective, as they create imputed cell counts less than observed partial counts.” Cox and Better 
develop version of raking that fixes this shortcoming 

 Obtaining a sample of the solution-feasible space is goal for future research. If probabilities of selection of each 

“point” in the solution-feasible space were known, one could calculate the variance due to imputation, confidence 

intervals, and related quantities. 

Conclusion

 This session has provided three very different applications of sampling, yet each is very innovative in its own 

way. 

 

Acknowledgements: I sincerely thank the authors/presenters not only for their excellent presentations but also for 

their well prepared papers given to me in advance. Very special thanks to Dale Atkinson for organizing the session, 

chairing it, and inviting me to discuss. 

References 

Pierre Lavallée and Michael A. Hidiroglou, On the Stratification of Skewed Populations, Survey Methodology, 

1988, Vol. 14, No. 1, 33-43 

 

Patricia Gunning and Jane M. Horgan, A New Algorithm for the Construction of Stratum Boundaries in Skewed 

Populations, Survey Methodology, 2004, Vol. 30 , No. 2, 159-166