Two Measures for Sample Size Determination

Abstract

Social surveys often must estimate the sizes or the proportions of many small groups and differences among them. The discussion of the needed precision of the estimators and the corresponding sample size is difficult, in particular when lay persons are involved. Two measures are developed which help in this discussion of the precision. These measures are called precision resolutions. The first of these measures, the size resolution, is derived from approximations to the probability of not observing a group in a sample and the second measure, the difference resolution, addresses the difference of two proportions. The precision resolutions are operationalisations of the smallest group or difference which can be estimated from a sample. Since they embody elements of statistical hypothesis tests without the need of a complete test specification they are simple to specify and nevertheless contain the necessary elements for sample size determination. The precision resolutions lead to the determination of the sample size for simple random samples but extensions to more complex samples are possible with the help of the design effect. The precision resolutions were developed for the planning of the Swiss Population Survey and this survey as well as the European Social Survey serve as examples of their application.