Selection of Strata Sample Sizes for the Comparison of Domain Means

Abstract

In a sample survey, comparisons among the means of several domains of study are often of primary importance. Assuming stratified random sampling, this article investigates strata sample size allocations to optimize the precision with which the comparisons will be made. Specifically, we determine the optimal allocation of a total sample of size n among the strata by (a) maximizing for fixed n the probability, P , that specified variance constraints are satisfied, and (b) minimizing the total sample size n for a desired level of P, P *. Both exact and approximate solutions are presented and compared using a sequence of numerical examples. This numerical study is for the important special case of two domains. Finally, there is a numerical assessment of the effect on the optimal allocation of incorrect specifications of the design parameters.