Journal of Mathematics and Statistics

A Monte Carlo Study of Seven Homogeneity of Variance Tests

Howard B. Lee, Gary S. Katz and Alberto F. Restori

DOI : 10.3844/jmssp.2010.359.366

Journal of Mathematics and Statistics

Volume 6, Issue 3

Pages 359-366

Abstract

Problem statement: The decision by SPSS (now PASW) to use the unmodified Levene test to test homogeneity of variance was questioned. It was compared to six other tests. In total, seven homogeneity of variance tests used in Analysis Of Variance (ANOVA) were compared on robustness and power using Monte Carlo studies. The homogeneity of variance tests were (1) Levene, (2) modified Levene, (3) Z-variance, (4) Overall-Woodward Modified Z-variance, (5) O’Brien, (6) Samiuddin Cube Root and (7) F-Max. Approach: Each test was subjected to Monte Carlo analysis through different shaped distributions: (1) normal, (2) platykurtic, (3) leptokurtic, (4) moderate skewed and (5) highly skewed. The Levene Test is the one used in all of the latest versions of SPSS. Results: The results from these studies showed that the Levene Test is neither the best nor worst in terms of robustness and power. However, the modified Levene Test showed very good robustness when compared to the other tests but lower power than other tests. The Samiuddin test is at its best in terms of robustness and power when the distribution is normal. The results of this study showed the strengths and weaknesses of the seven tests. Conclusion/Recommendations: No single test outperformed the others in terms of robustness and power. The authors recommend that kurtosis and skewness indices be presented in statistical computer program packages such as SPSS to guide the data analyst in choosing which test would provide the highest robustness and power.

Copyright

© 2010 Howard B. Lee, Gary S. Katz and Alberto F. Restori. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.