The Choice of Subsample Size in Two-Stage Sampling

Abstract

This article presents a simple method for choosing the subsample size m in two-stage sampling when the values of the relevant design parameters, the variance ratio and the cost ratio, are not known exactly but can only be assumed to lie within some specific range. Measuring the efficiency of a choice of m by its precision relative to the optimum choice, which depends on the parameters, it is proposed to choose m so that its minimum efficiency, over the specified range of parameters, is maximized. The value of m under this maximin criterion, and its minimum efficiency, are derived. A simple practical rule is also given. The usefulness of the method is discussed and illustrated with examples.