Multiple comparisons of three ordered normal means for unbalanced models

Abstract

In this paper attention is directed towards the unbalanced one-way analysis of variance model with three populations, where the treatment means are known to satisfy the simple ordering μ 1≤ μ 2≤ μ 3. The problem of constructing simultaneous one-sided confidence intervals for the ordered pairwise differences of the treatment means μ 3 − μ 2, μ 3 − μ 1 and μ 2 − μ 1, is considered. A method of obtaining the exact critical points required by the confidence intervals is described, and some exact critical points are tabulated for small sample sizes. More generally, a method of obtaining tight conservative critical points is presented, and these conservative critical points are tabulated to cover all possible sample sizes.