Approximate probability integrals and critical values for Bartholomew's test for ordered means

Abstract

SUMMARY Critical values for Bartholomew's test of the equality of means against an alternative of simple order are available only in special cases when the number of groups exceeds four. In this paper a Taylor expansion of the null distribution of the test statistic is developed, from which adjusted critical values in the general case are derived. The adequacy of the approximation is examined when the number of groups is four or six.