The Kruskal-Wallis Test and Stochastic Homogeneity

A. Vargha, Harold D. Delaney

Research output: Contribution to journalArticle

78 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)170-192
Number of pages23
JournalJournal of Educational and Behavioral Statistics
Volume23
Issue number2
Publication statusPublished - 1998

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homogeneity
equality

Keywords

  • ANOVA
  • Friedman's g test
  • Kruskal-wallis h test
  • Mann-whitney test
  • Measure of stochastic superiority
  • Nonparametric anova
  • Stochastic equality
  • Stochastichomogeneity

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Education

Cite this

The Kruskal-Wallis Test and Stochastic Homogeneity. / Vargha, A.; Delaney, Harold D.

In: Journal of Educational and Behavioral Statistics, Vol. 23, No. 2, 1998, p. 170-192.

Research output: Contribution to journalArticle

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