Multiple Decision Procedures Based on Ranks for Certain Problems in Analysis of Variance

Abstract

This paper is concerned with single-sample multiple-decision procedures based on the ranks of the observations for selecting from $c$ continuous populations (a) the "best $t$" populations without regard to order, (b) the "best $t$" populations with regard to order, and (c) a subset which contains all populations "as good or better than a standard one." The "bestness" of a population is characterised by its location parameter; the best population being the one having the largest location parameter; the second best being the one having the second largest location parameter, etc. Large-sample methods are provided for computing the sample sizes necessary to guarantee a preassigned probability of correct grouping (or ranking) under specified conditions on location parameters. It is shown that the asymptotic efficiency of these procedures relative to the normal theory procedures (see, for example, Bechhofer [1] and Gupta and Sobel [3]) is the same as that of the associated tests in one-way analysis of variance model I problem. If the ratio of the sample sizes is equal to this efficiency, the two procedures being compared are shown to have the same asymptotic performance characteristic. Finally, in the case of problem (c) two alternative rank-score procedures are proposed which are asymptotically equi-efficient.