A non-parametric analysis of variance to test two or more independent samples in a given data set.
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 (ANOVA) wherein the assumption of normality 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 (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; when systematic variable used for ranking is continuous, each of the k samples are randomly selected from the populations it represents and are independent samples, the probability distributions underlying the sample are identical in their shape and at least each independent sample has a size of 5 or more.
• Mann–Whitney U test
• Friedman test