Kruskal–Wallis one-way analysis of variance

The Kruskal -Wallis test (after William Kruskal and Wilson Allen Wallis, and H - Test) is a parameter-free statistical test, is tested with the in the context of analysis of variance, whether independent samples ( groups or sets of measurements) in terms of ordinal variable of a common population come. It resembles a Mann-Whitney U-test and is based on how this rank order totals, with the difference that it can be applied for the comparison of more than two groups.

The null hypothesis H0 is: there is no difference between the groups. As a test statistic of the Kruskal -Wallis test, a so-called H- value is calculated. The H value is formed as follows: The rank for each of the observations in the union of the sample is determined. From then the rank sums for each group and from the test statistic

Or in the presence of bonds

( with the number of bound observations with rank ) is calculated. This follows under the null hypothesis a chi -square distribution. The degrees of freedom ( df ) are calculated according to Df = k-1, where k is the number of classes ( groups). The calculated test statistic H is compared with a theoretical size of the chi -square distribution for a selected type 1 error. H is the calculated value is greater than the H value of the chi-squared table that H0 is discarded, so there is a significant difference between the groups.

If and, then the test statistic is non- distributed and it has to be resorted to tabulated critical values ​​.

A similar test such as the Kruskal -Wallis test is the Jonkheere - Terpstra test or its generalization, the umbrella test after Mack and Wolfe. An extension of the Kruskal- Wallis test to the scope of the multifactorial analysis of variance is the Scheirer Hare -ray test.