Purpose

   This procedure compares multiple independent samples. It runs Kruskal-Wallis ANOVA by Ranks and Median Test.

Preparations

    Run Statistics→Nonparametric Statistics →Comparing multiple independent samples.... command.

Results

Kruskal-Wallis ANOVA.
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. Criterion statistic H has Chi-square distribution with k - 1 (where k - groups count) degrees of freedom.

H =
H (adjusted) =

Median test.
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, StatPlus 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.