On two-stage selection procedures and related probability-inequalities

In this paper we discuss a modification of the Dudewicz-Dalal procedure for the problem of selecting the population with the largest mean from k normal populations with unknown variances. We derive some inequalities and use them to lower-bound the probability of correct selection. These bounds are applied to the determination of the second-stage sample size which is required in order to achieve a prescribed probability of correct selection. We discuss the resulting procedure and compare it to that of Dudewicz and Dalai (1975).