Construction of Decision Procedures for Selecting Populations

Abstract

Selection procedures are considered in a significance testing point of view. Recent results on the equivalence between selection procedures and multiple tests for a certain class of hypotheses are reviewed and then first applied to construct selection rules for choosing the best population. When under design aspects certain power requirements are incorporated, the classical indifference zone approach of Bechhofer as well as Gupta’s subset selection formulation can be shown to fit into this general framework. The equivalence results are moreover demonstrated to provide efficient stepwise procedures for the problem of selecting a subset of populations that contains all good ones. Treating this latter problem by imposing the additional requirement to select none of the bad populations leads to partitioning rules. Selection rules for the one-way layout under a normal distributional set-up are dealt with in detail, and the resulting numerical problems are discussed.