Partitioning Bernoulli Populations with Respect to a Control

Abstract

This article is concerned with the problem of partitioning a set of Bernoulli populations with respect to a control Bernoulli population, into two subsets according to their probabilities of success in a single trial. Two procedures are proposed. The first one is a single-stage procedure, based on Tong's single-stage procedure (1969) for partitioning normal populations. The second procedure is a two-stage procedure with elimination, based on Solanky's two-stage procedure (2006) for normal populations. The derivation of the probability of a correct decision and the least favorable configurations are exact, without making use of the normal approximation to the binomial.

Keywords:

• Bernoulli population
• Binomial distribution
• Least favorable configuration
• Probability of a correct decision
• Sample size

Mathematics Subject Classification:

• Primary 62F07
• Secondary 62P30, 62P10, 62L05

Acknowledgments

The authors wish to thank the Editor and referees for their helpful comments that led to a considerable improvement of this article. This research was supported in part by a research grant that the first author received from the University of North Florida.