A COMPARATIVE ANALYSIS FOR HOMOGENEITY OF VARIANCE TESTS

Abstract

The testing of homogeneity of variances has an important place in data analysis, especially in determining the test statistics in the analysis of variance. If the F test, which is a parametric technique, is desired to be used as test statistics in variance analysis, group variances should be homogeneous. To test for homogeneity of variance, several tests can be used. The non-parametric tests among these do not require the assumption that the groups are normally distributed. In this study, the performance of five different non-parametric tests for homogeneity of variances which are mean-based Levene, median-based Levene also known as Brown-Forsyte, trimmed-mean-based Levene, Fligner-Killeen, and nonparametric Levene tests, are investigated in terms of empirical type 1 error rates and powers for different sample sizes and various symmetric and asymmetric distributions by Monte Carlo simulation studies with free and open-source software R. The simulation results show that the Brown Forsyte test generally has the lowest type-1 error rates while the Median-based Levene test has the highest power for both symmetric and asymmetric distributions in most cases.