GRE (Graduate Record Examinations) Psychology Measurement and Methodology-Statistical Procedures Study Material (Page 1 of 24)

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Kruskal-Wallis Test: Assumptions


Kruskal-Wallis test is a one-way ANOVA ranks developed by William Kruskal and W. Allen Wallis. This is a non-parametric test used to examine whether the given sample originates from the same distribution and compare two or more independent samples of equal or different sample sizes. The one-way analysis of variance is the equivalent of Kruskal-Wallis test.

The stochastic dominance of one sample over the other sample is indicated by the Kruskal-Wallis test. But the test fails to examine where the stochastic dominance take place in the sample or for how many pairs in the sample are stochastically dominated. To understand about the stochastic dominance specifically, some other tests are used.


To apply

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Kruskal-Wallis Test: Method of the Test


First step is to rank the data from all the groups, starting from one to N. Then add the ranks of sample.

Then calculate the value by applying the following formula:


= sum of sample sizes for all samples

= number of samples

= sum of ranks in the sample

= size of the sample

  • Next step is to calculate the critical chi-square value, wh

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