article · Advances in Methodology and Statistics
Standard statistical analyses often rely on the one-way analysis of variance F-test, which assumes that data follow a normal distribution and display equal variance across groups. When these conditions are violated, test performance can decline. Through extensive computer simulations evaluating 184 distinct scenarios across equal and unequal variances and group means, the statistical power of the parametric F-test was compared directly against the non-parametric Kruskal-Wallis test. In the vast majority of non-normal conditions, the Kruskal-Wallis test demonstrated superior power over the F-test. While the F-test performed slightly better when data met normal distribution assumptions, the performance advantage was not statistically significant. Consequently, the Kruskal-Wallis test proves to be a safer and more robust analytical option whenever the underlying distributional properties of experimental data are uncertain.
Researchers across diverse disciplines frequently compare multiple groups to detect differences. Choosing an unsuitable statistical test when data violate underlying assumptions can lead to unreliable findings. This research demonstrates that non-parametric methods provide dependable statistical power without sacrificing significant performance, offering analysts confidence even when working with irregular or non-normal experimental datasets.
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The effects of the violations of normality and homogeneity of variances assumptions on the power of the one-way ANOVA F-test is studied in this paper. Simulation experiments were conducted to compare the power of the parametric F-test with the non-parametric Kruskal‒Wallis (KW) test in normal/non-normal, equal/unequal variances scenarios and equal/unequal sample group means. Each of these 184 simulation experiments was replicated N = 1000 times and power obtained for both F and KW tests. The Shapiro‒Wilk's test for normality and Bartlett's/Levene's tests for homogeneity of variances was conducted in each experiment. Results show that the power of the KW tests outperformed those of the F-tests in the 92 (85/92) non-normal cases. Although the power of the F-tests is higher than those of the KW tests in 85 out of the 92 experiments under normality assumptions, these differences, in all cases in this study are not significant (p > 0.05) using both t and sign tests. Based on these results, this study favours the KW test as a more robust test and safer to use rather than the F-test especially when the distributional assumptions of data sets are in doubt.
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DOI: 10.51936/ltgt2135
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