On Two-Stage Multiple Comparison Procedures When there are Unequal Sample Sizes in the First Stage

Abstract

A problem of considerable practical importance when applying multiple comparison procedures is that unequal variances can seriously affect power and the probability of a Type I error. A related problem is getting a precise indication of how many observations are required so that the length of the confidence intervals will be reasonably short. Two-stage procedures have been proposed that give an exact solution to these problems, the first stage being a pilot study for the purpose of obtaining sample estimates of the variances. However, the critical values of these procedures are available only when there are equal sample sizes in the first stage. This paper suggests a method of evaluating the experimentwise Type I error probability when the first stage has unequal sample sizes.