Kruskal-Wallis test

Examples of Kruskal-Wallis test in the following topics:

• Rank Randomization: Two or More Conditions (Kruskal-Wallis)

  • The Kruskal-Wallis test is a rank-randomization test that extends the Wilcoxon test to designs with more than two groups.
  • It tests for differences in central tendency in designs with one between-subjects variable.
  • The test is based on a statistic H that is approximately distributed as Chi Square.
  • Finally, the significance test is done using a Chi Square distribution with k-1 degrees of freedom.

• Kruskal-Wallis H-Test

  • The Kruskal–Wallis one-way analysis of variance by ranks is a non-parametric method for testing whether samples originate from the same distribution.
  • The Kruskal–Wallis one-way analysis of variance by ranks (named after William Kruskal and W.
  • The parametric equivalent of the Kruskal-Wallis test is the one-way analysis of variance (ANOVA).
  • When the Kruskal-Wallis test leads to significant results, then at least one of the samples is different from the other samples.
  • Since it is a non-parametric method, the Kruskal–Wallis test does not assume a normal distribution, unlike the analogous one-way analysis of variance.

• Comparing Two Populations: Independent Samples

  • Nonparametric independent samples tests include Spearman's and the Kendall tau rank correlation coefficients, the Kruskal–Wallis ANOVA, and the runs test.
  • Nonparametric methods for testing the independence of samples include Spearman's rank correlation coefficient, the Kendall tau rank correlation coefficient, the Kruskal–Wallis one-way analysis of variance, and the Walk–Wolfowitz runs test.
  • The Kruskal–Wallis one-way ANOVA by ranks is a nonparametric method for testing whether samples originate from the same distribution.
  • When the Kruskal–Wallis test leads to significant results, then at least one of the samples is different from the other samples.
  • Since it is a non-parametric method, the Kruskal–Wallis test does not assume a normal distribution, unlike the analogous one-way analysis of variance.

• When to Use These Tests

  • Some kinds of statistical tests employ calculations based on ranks.

• Distribution-Free Tests

  • Anderson–Darling test: tests whether a sample is drawn from a given distribution.
  • Kruskal-Wallis one-way analysis of variance by ranks: tests whether more than 2 independent samples are drawn from the same distribution.
  • Median test: tests whether two samples are drawn from distributions with equal medians.
  • Sign test: tests whether matched pair samples are drawn from distributions with equal medians.
  • Squared ranks test: tests equality of variances in two or more samples.