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.