An Empirical Comparison of the Anova F-Test, Normal Scores Test and Kruskal-Wallis Test Under Violation of Assumptions
1974/12/01 by Betty J. Feir-Walsh, Betty J. Feir‐Walsh, Larry E. Toothaker · 146 citations
Decision Sciences · Mathematics · Psychology · #Analysis of variance #Anderson–Darling test #Combinatorics #Econometrics #Empirical research #F-test #Forecasting Techniques and Applications #Goldfeld–Quandt test #Kolmogorov–Smirnov test #Kruskal's algorithm #Kruskal–Wallis one-way analysis of variance #Mann–Whitney U test #Mathematics #Normality test #Psychology #Statistical hypothesis testing #Statistics #Test (biology) #Test statistic #Z-test
paper · open access · doi:10.1177/001316447403400406
published in Educational and Psychological Measurement 34(4), 789-799 (SAGE Publishing)
openalex publication_date 1974/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract
The present research compares the ANOVA F-test, the Kruskal-Wallis test, and the normal scores test in terms of empirical alpha and empirical power with samples from the normal distribution and two exponential distributions. Empirical evidence supports the use of the ANOVA F-test even under violation of assumptions when testing hypotheses about means. If the researcher is willing to test hypotheses about medians, the Kruskal-Wallis test was found to be competitive to the F-test. However, in the cases investigated, the normal scores test was not consistently better than the F-test or the Kruskal-Wallis test and could not be recommended on the basis of this research.
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