Sample Sizes for Comparison of Proportions

Abstract

This paper examines the problem of determining sample sizes for comparing sample proportions from n independent binomial populations under the null hypothesis that the population proportions are different. For specified precisions and sampling costs, it is shown that the problem of determining optimal sample sizes can be formulated as a convex programming problem. In addition, the problem of obtaining the best precision within a budgeted cost of sampling is examined. This methodology is illustrated with an example application.

KEYWORDS:

• Comparison of proportions
• Significant differences
• Nonlinear programming