An Empirical Comparison of Several Multiple Range Tests for Variances

Abstract

Four multiple range tests for specifying homogeneous subsets of treatment variances are proposed and investigated. The procedures are based on Hartley's F-max statistic, Cochran's statistic, Bartlett and Kendall's normalizing log transformation of the sample variances, and Box's approximate test. The philosophy underlying these tests, with respect to Type-I errors, is that advocated by Newman and later by Keuls. Empirical significance levels are obtained by simulating independent random samples from normal, uniform, double exponential and Cauchy distributions. The Box test was the only procedure not seriously affected by nonnormality.