# Nonparametrics Statistics Notes - Kruskal-Wallis ANOVA by Ranks and Median Test

These two tests are nonparametric alternatives to between-groups one-way analysis of variance. STATISTICA expects the data to be arranged in the same way as you would arrange a data file for an analysis with ANOVA/MANOVA. Specifically, the data file should contain a coding variable with codes to uniquely identify the group membership of each case. Up to 10 groups can be compared.

Select Comparing multiple indep. samples (groups) on the Nonparametric Statistics Startup Panel - Quick tab to display the Kruskal-Wallis ANOVA and Median Test dialog box, in which you select the coding variable and a dependent variables list (variables on which the groups are to be compared), and the codes used in the coding variable for identifying the different groups that are to be compared.

Assumptions and interpretation. The Kruskal-Wallis ANOVA by Ranks test assumes that the variable under consideration is continuous and that it was measured on at least an ordinal (rank order) scale. The test assesses the hypothesis that the different samples in the comparison were drawn from the same distribution or from distributions with the same median. Thus, the interpretation of the Kruskal-Wallis test is basically identical to that of the parametric one-way ANOVA, except that it is based on ranks rather than means.

The Median test is a "crude" version of the Kruskal-Wallis ANOVA in that it frames the computation in terms of a contingency table. Specifically, STATISTICA will simply count the number of cases in each sample that fall above or below the common median, and compute the Chi-square value for the resulting 2 x k samples contingency table. Under the null hypothesis (all samples come from populations with identical medians), we expect approximately 50% of all cases in each sample to fall above (or below) the common median. The Median test is particularly useful when the scale contains artificial limits, and many cases fall at either extreme of the scale ("off the scale"). In this case, the Median test is in fact the only appropriate method for comparing samples.

See Kruskal-Wallis ANOVA and Median Test - Quick tab for further details.