Testing homogeneity of ordered variances

Summary

Fujino (1979) studied several tests for homogeneity of nondecreasing variances and concluded that the modification of Bartlett’s (1937) test, first proposed by Boswell & Brunk (1969), is generally superior to its competitors in terms of power. A weakness of this test, however, is that the null distribution of the test statistic has not been adequately determined for cases other than when the group sample sizes are equal. In this article a class of simple tests for equality of non-decreasing variances is proposed which can be used without special tables for arbitrary sample sizes. Some of these tests have operating characteristics which compare favorably to those of the modification of Bartlett’s test. A prescription is also given for applying the tests in cases where the population variances are constrained by more general partial orders.