Selecting the Best Population, Provided it is Better than a Standard: The Unequal Variance Case

Abstract

Bechhofer and Turnbull (1978) proposed two procedures for selecting the best treatment that is better than a standard. That is, the procedures guarantee that (a) with probability at least P ₀* (specified), no population is selected when the largest population mean is sufficiently less than the standard and (b), with probability at least P ₁* (specified), the population with the largest mean is selected when that mean is sufficiently greater than the second largest mean and the standard. Their first procedure solved the problem for the case of known variances, and the second was for the case of unknown but equal variances. They suggested that the unequal variance case might be handled by using the method in Rinott (1978), but no details were given. This article provides the appropriate probability equations and the necessary table.

Key Words:

• Ranking and selection
• Two-stage procedure