Approximating the Probability of Selecting the Best Treatment With A Heteroscedastic Procedure When The First Stage Has Unequal Sample Sizes

Abstract

Consider k normal distributions having meansμ ₁,...,μ_k and variances σ² ₁,..., σ² _k . Let μ_[1]≥...≥ μ_[k] be the means written in ascending order. Dudewicz and Dalai proposed a two-stage procedure for selecting the population having the largest mean μ_[k] where the variances are assumed to be unknown and unequal. This paper considers an approximate but conservative solution for situations where unequal sample sizes are used in the first stage. The paper also considers how to estimate the actual probability of selecting the “best” treatment; that is, the one having mean μ_[k], after a heteroscedastic ANOVA has been performed.