ASYMPTOTIC APPROXIMATIONS OF THE NULL DISTRIBUTION OF THE ONE-WAY ANOVA TEST STATISTIC UNDER NONNORMALITY

Abstract

This paper is concerned with the null distribution of the one-way ANOVA test statistic T for testing the equality of means of q nonnormal populations with common variance. It is known that the null distribution of T converges to X²_q-1 when all the sample sizes of the q populations are large. We extend this result by obtaining the Bartlett correction and an asymptotic expansion under general conditions. Numerical accuracies are studied for some approximations of the percentage points and actual test sizes of T based on the limiting distribution, Bartlett correction and an asymptotic expansion.