## Kruskalwallis Test Oneway Anova By Ranks

The Kruskal-Wallis test is a nonparametric analog to the one-way analysis of variance discussed in Chapter 13. It is a simple generalization of the Wilcoxon rank-sum test. The problem is to identify whether or not three or more populations (independent samples) have the same distribution (or central tendency). We test the null hypothesis (H0) that the distributions of the parent populations are the same against the alternative (H1) that the distributions are different. The rationale for the test involves pooling all of the data and then applying a rank transformation. If the null hypothesis is true, each group should have rank sums that are similar. If at least one group has a higher (or lower) median than the others, it should have a higher (or lower) rank sum. Table 14.8 provides an example of data layout for several samples (e.g., k samples), following the model for the Kruskal-Wallis test.

To describe the test procedure, we need to use some mathematical notation. Let Xtj represent the jth observation from the ith population. We assume that there are k > 3 populations and for population i we have n, observations. N = the total number

 TABLE 14.8. Data Layout for Kruskal-Wallis Test Observation Sample 1 Sample 2 . . . Sample k