Comparing Welch's ANOVA, a Kruskal-Wallis test and traditional ANOVA in case of Heterogeneity of Variance
Master of Science
Dr. Wen Wan
Dr. Donna McClish
Dr. Qin Wang
Analysis of variance (ANOVA) is a robust test against the normality assumption, but it may be inappropriate when the assumption of homogeneity of variance has been violated. Welch ANOVA and the Kruskal-Wallis test (a non-parametric method) can be applicable for this case. In this study we compare the three methods in empirical type I error rate and power, when heterogeneity of variance occurs and find out which method is the most suitable with which cases including balanced/unbalanced, small/large sample size, and/or with normal/non-normal distributions.
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F-test in analysis of variance is unsuitable in three-group heterogeneity cases, even though it is a robust test when data are homogeneous, normal and equal/unequal sample sizes.
Welch’s test performs the best in three-group heterogeneity cases when data are normal and equal and unequal sample sizes. And this result is consistent with the results from Moder (2010) that Welch’s F-test is useful for a small number of group cases.
Kuskal-Wallis test is acceptable in mild heterogeneity cases when data are normal and equal sample sizes.