Some suggestions about appropriate use of the Kruskal–Wallis test

In behavioural research, analysis of variance (ANOVA) remains a popular statistical technique (see the survey of Ruxton & Beauchamp 2008). ANOVA compares a univariate measure between samples from two or more populations. To use ANOVA appropriately, researchers must assume that the distributions of the measure for each sample are normal and have equal variance. The ANOVA then tests the null hypothesis that the mean values of the measurement in the two or more populations from which the samples are drawn are the same. Here, we wish to highlight confusion that has arisen in the application of the KruskaleWallis test (hereafter abbreviated to KWt), which is often (but misleadingly) described as the nonparametric alternative to ANOVA. The KWt and its equivalent for two samples (generally called the ManneWhitney U test) are probably the nonparametric tests that are most widely used in behavioural sciences. However, it appears that misapplication of the KWt is widespread; hence we begin by defining carefully how this test can be used appropriately. We then briefly demonstrate areas of apparent misunderstanding. Lastly, we offer clear guidance on the use of ANOVA and the KWt and how researchers can select and apply the most appropriate test for their situation.

[1]  H. Büning.  Robustness and power of parametric, nonparametric, robustified and adaptive tests—The multi-sample location problem , 2000 .

[2]  Ronald C. Serlin,et al.  QUANTITATIVE METHODS IN PSYCHOLOGY Comparison of ANOVA Alternatives Under Variance Heterogeneity and Specific Noncentrality Structures , 1986 .

[3]  Ralph A. Alexander,et al.  A New and Simpler Approximation for ANOVA Under Variance Heterogeneity , 1994 .

[4]  G. Beauchamp,et al.  Time for some a priori thinking about post hoc testing , 2008 .

[5]  B. Tóthmérész,et al.  Measures of sociality: two different views of group size , 2008, Animal Behaviour.

[6]  Harold D. Delaney,et al.  The Kruskal-Wallis Test and Stochastic Homogeneity , 1998 .

[7]  T. C. Oshima,et al.  Type I error rates for James's second-order test and Wilcox's Hm test under heteroscedasticity and non-normality , 1992 .

[8]  E. Kasuya.  Mann–Whitney U test when variances are unequal , 2001, Animal Behaviour.

[9]  G. Beauchamp,et al.  Vigilance in Greater Flamingos Foraging at Night , 2003 .

[10]  S. Julious.  Why do we use pooled variance analysis of variance? , 2005 .

[11]  Robert W. Day,et al.  Comparisons of Treatments After an Analysis of Variance in Ecology , 1989 .

[12]  Holger Dette,et al.  Box-Type Approximations in Nonparametric Factorial Designs , 1997 .

[13]  S. Rust,et al.  A modification of the kruskal-wallis statistic for the generalized behrens-fisher problem , 1984 .

[14]  J. Algina,et al.  Univariate and Multivariate Omnibus Hypothesis Tests Selected to Control Type I Error Rates When Population Variances Are Not Necessarily Equal , 1996 .