Empirical Comparison of the Kruskal Wallis Statistics and its Parametric Counterpart

The nonparametric Kruskal-Wallis statistics (H-test) and its parametric counterpart, the one way ANOVA (F-test) are two powerful statistics commonly used to compare k (>2) sample. The Monte Carlo approached was used in this study to compare the performances of the two statistics especially when the assumptions of normality and homogeneity of variance are violated. Data were generated from normal, exponential and Poisson distributions. It was discovered that when the samples are from normal and Poisson distributions, the F-test is more powerful than the H-test but the reverse is the case when they are from exponential distribution. However, when the sample size increases to say ≥15, the two statistics perform equally well in terms of their power irrespective of the distribution from which the samples are drawn.