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

University of Southern California and Center for the Study of Evaluation, UCLA

Consider k normal distributions having meansµ₁...,µ_k and variances ²₁..., ²_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.

Key Words: Ranking in selection • Indifference zone

Journal of Educational and Behavioral Statistics, Vol. 8, No. 1, 45-58 (1983)
DOI: 10.3102/10769986008001045


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