Bivariate inductive statistics - ordinal and nominal variables - independent groups

Kruskal-Wallis test, Westenberg-Mood median test

Kruskal-Wallis test compares the medians of three or more groups. It tests the null hypothesis that the different samples in the comparison were drawn from distributions with the same median. Alternative hypothesis states that at least one median is different from the rest. Kruskal-Wallis test uses ranks instead of original data (1 is assigned to lowest value etc.) Test assumes at least ordinal variable, the population variances are equal, the groups are independent and all groups are simple random samples from their respective populations (each individual in the population has an equal probability of being selected in the sample).

In the case of unequal variances Westenberg-Mood median test should be used. Median test is more general but less powerful alternative to the Kruskal-Wallis H test for testing if several independent samples come from the same population. It tests whether two or more independent samples differ in their median values for a criterion variable. The samples are combined temporarily to determine their pooled median value. A table can then be constructed in which the columns are the samples and the two rows reflect the sample counts above or below the pooled median value. The significance is calculated using chi-square statistic.

Example: Does depend education achieved on place of birth?