The Kruskal-Wallis Test and Stochastic Homogeneity

András Vargha and Harold D. Delaney

Journal of Educational and Behavioral Statistics, 1998, vol. 23, issue 2, 170-192

Abstract: For the comparison of more than two independent samples the Kruskal-Wallis H test is a preferred procedure in many situations. However, the exact null and alternative hypotheses, as well as the assumptions of this test, do not seem to be very clear among behavioral scientists. This article attempts to bring some order to the inconsistent, sometimes controversial treatments of the Kruskal-Wallis test. First we clarify that the H test cannot detect with consistently increasing power any alternative hypothesis other than exceptions to stochastic homogeneity. It is then shown by a mathematical derivation that stochastic homogeneity is equivalent to the equality of the expected values of the rank sample means. This finding implies that the null hypothesis of stochastic homogeneity can be tested by an ANOVA performed on the rank transforms, which is essentially equivalent to doing a Kruskal-Wallis H test. If the variance homogeneity condition does not hold then it is suggested that robust ANOVA alternatives performed on ranks be used for testing stochastic homogeneity. Generalizations are also made with respect to Friedman’s G test.

Keywords: Keywords: ANOVA; Friedman’s G test; Kruskal-Wallis H test; Mann-Whitney test; measure of stochastic superiority; nonparametric ANOVA; stochastic equality; stochastic homogeneity (search for similar items in EconPapers)
Date: 1998
References: Add references at CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
https://journals.sagepub.com/doi/10.3102/10769986023002170 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:23:y:1998:i:2:p:170-192

DOI: 10.3102/10769986023002170

Access Statistics for this article

More articles in Journal of Educational and Behavioral Statistics
Bibliographic data for series maintained by SAGE Publications ().