Levene's Test for Relative Variation

Abstract

Forms of Levene's test for evaluating relative variation (univariate) are compared by simulation, along with the F-test of ratios of squared coefficients of variation, the F-test of ratios of variances of logarithms, and Bartlett's test on logarithms. Only the Levene's tests using the medians were always robust. These consisted of transforming each of a set of sample variates Xi to Yi = | Xi − Md(Xi) | /Md(Xi) or to Yi = | In Xi − Md(ln Xi) | for comparison by ANOVA, where the Md's represent the medians. The use of medians with the log transformation was slightly more powerful when the underlying distributions were positively skewed, while the use of the untransformed ratio form of the test was slightly more powerful when the distributions were symmetrical or negatively skewed. Recommendations and some problems that remain are discussed.