A New Procedure for Selecting a Subset Containing the Best Normal Population

Abstract

A new procedure, called the fiducial procedure, is defined for selecting a subset of a collection of normal populations with common known variance. In the presence of an “indifference zone,” this procedure has probability at least P * of selecting the “best” population. An upper bound is obtained for the smallest indifference zone d * that satisfies the P * condition. Comparisons of relative merit are made between the fiducial procedure, Gupta's (1965) procedure, and an appropriate modified version of Gupta's procedure. Some ad hoc methods are presented for implementing the techniques of the fiducial procedure from a Bayesian approach.