# Kruskal-Wallis Test

**Definition**

*noun*

A non-parametric analysis of variance to test two or moreindependent samples in a given data set.

**Supplement**

It was named after William Kruskal and W. Allen Wallis.

**Kruskal-Wallis** test does not assume a normal distribution of residuals since it is a non-parametric method unlike in parametric one way analysis of variance (ANOVA) wherein the assumption ofnormality or equality of variance are met.

This non-parametric test is used when the data have *k*independent samples in order to decide if the samples come from a distinct population or if at least one sample comes from a different population as regard to the position parameters.

**H** is the test statistic of** Kruskall-Wallis** test. This value is evaluated to the table of critical values for U based on the sample size of each group. If the results shows that H exceeds the critical value at some significance level (usually 0.05) it indicates that there is a proof to reject the null hypothesis in favor of the alternative hypothesis. When rejecting the null hypothesis, then at least one of sample is stochastically dominates to the other sample.

Some assumptions to be consider when using this test are; whensystematic variable used for ranking is continuous, each of the *k* samples arerandomly selected from the populations it represents and areindependent samples, the probability distributions underlying the sample areidentical in their shape and at least eachindependent sample has a size of 5 or more.

**Compare:**

• One-way Analysis of Variance (ANOVA)

**See also:**