Overview

We covered one-way between-subjects ANOVA in Chapter 23. Among other assumptions of ANOVA are that the scale of measurement underlying the dependent variable is at least an approximation to interval (i.e., it is meaningful to compute means and standard deviations) and that the dependent variable distributions within the groups are relatively normal. If the distributions departed substantially from the normality assumption and if the researchers did not choose to subject their data to a nonlinear transformation, or if the researchers collected ranked data, then they can opt to use a distribution-free nonparametric analogue to the one-way between-subjects ANOVA.

The nonparametric analogues to One-Way ANOVA

We briefly treat two of the most commonly used nonparametric analogues to a one-way between-subjects ANOVA: the median test and the Kruskal–Wallis test. In both cases, there are two or more independent groups of cases that have been assessed on a dependent variable that reaches at least ordinal measurement.

The median test

The median test is a relatively imprecise test, in the sense that a good deal of the information in the data is discarded in the computation. Its advantage is that it is relatively simple to compute, a modest advantage indeed in computer-based data analysis. For the purposes of the analysis, the data for all groups are momentarily combined so that a median of the entire set of scores is computed. It is then simply determined how many scores in each group are above and below that common median.