On uncertainty of a proportion from a stratified random sample of a small population

Abstract

This article considers the uncertainty of a proportion based on a stratified random sample of a small population. Using the hypergeometric distribution, a Clopper–Pearson type upper confidence bound is presented. Another frequentist approach that uses the estimated variance of the proportion estimator is also considered as well as a Bayesian alternative. These methods are demonstrated with an illustrative example. Some aspects of planning, that is, the impact of specified strata sample sizes, on uncertainty are studied through a simulation study.

Keywords:

• Bayesian
• Clopper–Pearson
• frequentist
• hypergeometric distribution
• simultaneousinference
• upper confidence bound
• variance

Acknowledgments

We thank C.C. Essix for her support and encouragement of this work. We also thank Dave Collins, Scott Vander Wiel and the anonymous referees for helpful and insightful comments on an earlier version.

Disclosure statement

No potential conflict of interest was reported by the authors.