It is shown that the procedure of applying the Wilcoxon test after Levene's transformation can have an inflated Type I error rate when distributions are skewed. Thus, when the data may come from an asymmetric distribution, the Wilcoxon test should not be applied as a test for homogeneity of variances after Levene's transformation.
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References
1.
BlairR. C.HigginsJ. J.SmitleyD. S. (1980) On the relative power of the U and t tests. British Journal of Mathematical and Statistical Psychology, 33, 114–120.
2.
BrownM. B.ForsytheA. B. (1974) Robust tests for the equality of variances. Journal of the American Statistical Association, 69, 364–367.
3.
LeveneH. (1960) Robust tests for equality of variances. In OlkinI.GhuryeS. G.HoeffdingW.MadowW. G.MannH. B. (Eds.), Contributions to probability and statistics. Stanford, CA: Stanford Univer. Press. Pp. 278–292.
4.
ManlyB. F. J.FrancisR. I. C. C. (2002) Testing for mean and variance differences with samples from distributions that may be non-normal with unequal variances. Journal of Statistical Computation and Simulation, 72, 633–646.
5.
SchultzB. (1983) On Levene's test and other statistics of variation. Evolutionary Theory, 6, 197–203.
6.
TalwarP. P.GentleJ. E. (1977) A robust test for the homogeneity of scales. Communications in Statistics–Theory and Methods, 6, 363–369.
7.
Van den BrinkW. P.van den BrinkS. G. J. (1989) A comparison of the power of the t test, Wilcoxon's test, and the approximate permutation test for the two-sample location problem. British Journal of Mathematical and Statistical Psychology, 42, 183–189.
