Exact Simultaneous Confidence Intervals for Pairwise Comparisons of Three Normal Means

Abstract

Abstract The problem of simultaneously estimating the pairwise differences of means of three independent normal populations with equal variances is considered. A computational method involving a bivariate t density is used to form confidence intervals with simultaneous coverage probability equal to 1 — a. For equal sample sizes, the method is the Tukey studentized range procedure. With unequal sample sizes, the method is superior to the various generalized Tukey methods. A table of probability points is presented for small sample sizes. A large-sample approximation based on the bivariate normal and studentized range distributions is given.