Robust post-hoc multiple comparisons: a study on Tukey test using Winsorized mean

Post-hoc multiple comparisons methods play a crucial role in determining differences in group means following one-way Analysis of Variances (ANOVA) performance. Traditionally relying on assumptions of normality and homogeneity of variance that is common in statistical analyses, this method faces challenges in datasets with prevalent heterogeneity of variances. Therefore, robust central tendency methods, such as the Winsorized mean, become significant in statistical analyses. This research introduces the O’Brien test, a standard tool for testing homogeneity of variances, incorporating Winsorized mean in scenarios where the assumptions of one-way ANOVA are violated. Consequently, the interpretation results of one-way ANOVA and Tukey’s test become more reliable. Simulation studies show that the proposed methodology is more preferable when dealing with non-normal distributions and moderately unequal variances. The comparison of power values of the test statistics leads to the conclusion that the modified approaches using robust estimators are more powerful than the classical approach.

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