On the Power of Tests for Multiple Comparison of Three Normal Means

Abstract

This article gives theoretical reasons for the findings of a simulation study by Shaffer (1981). Two well-established procedures for multiple comparison of three normal means are compared—an F procedure and an R procedure. It turns out that for a large set of parameters the average number of rejected pairwise hypotheses is larger when the F procedure is applied. To achieve our result we have to prove a special instance of a conjecture by David, Lachenbruch, and Brandis (1972).