A Monte Carlo Simulation Study for Comparing Performances of Some Homogeneity of Variances Tests

Hamit MIRTAGIOĞLU
Soner YIĞIT
Emel MENDEŞ
Mehmet MENDEŞ

Keywords

Homogeneity of variances, Anom test, Bartlett’s test, Levene’s test, Conover’s test, test power, type I error, simulation

Abstract

This simulation study has been carried out to compare empirical type I error and test power of five tests namely Anom, Bartlett's, Levene's, Brown-Forsythe, Anom, and Conover tests to check homogeneity of variances. For this purpose, a comprehensive Monte Carlo Simulation study has been carried out for different number of groups (k=3, 4, 5, and 10), variance ratios (i.e: 1, 5, 10, 15, and 20), and sample size combinations (equal and unequal sample sizes) under normality assumption. Based on results of 50,000 simulation, it is observed that the best robust tests are the Anom and Bartlett’s tests even if studying with very small sample size (n=5) and a large number of group cases (k=10). They were followed by the Levene’s and Conover tests in general. But, both the Conover and Levene’s tests have been slightly negatively affected from increases in the number of groups when sample sizes were small (n≤20). On the other hand, since the Brown-Forsythe test did not give satisfactory results for any of the experimental conditions, it was concluded that the use of this test should not be preferred for checking homogeneity of variance assumption. As a result, since the Anom and Bartlett’s are robust tests for all experimental conditions, it is possible to propose to the researcher to use this test to check homogeneity of variances assumption prior to ANOVA and t-test.