A revised generalized F-test for testing the equality of group means under non-normality caused by skewness

Abstract

The non-normality may occur in the data due to several reasons such as the presence of the outlier or skewness. It leads to lose the power and fail to control Type I error probability of the tests which are used to test the equality of the group means under heteroscedasticity. To overcome this problem, a revised generalized F-test (RGF) is proposed to test the equality of group means under heteroscedasticity in which non-normality caused by skewness in this study. An extensive Monte-Carlo simulation study is conducted to investigate the performance of the proposed test under several values of skewness for different number of groups. The proposed RGF is the best choice in the high level of skewness for k = 3, 4, 5. The Kruskal-Wallis test shows better performance than the others in small and moderate sample sizes for k = 6, and 7. It is shown that the proposed RGF test is superior than the non-parametric alternatives in the most of the conditions.

Keywords

• ANOVA
• generalized p-value
• non-normality
• skewed distribution
• penalized power
• doex

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