Kruskal–Wallis Test

The choice of an appropriate statistical test depends on the type of research questions being asked and the type of hypothesis being tested, and is closely contingent on key factors such as the type of outcome data being analyzed and the number of experimental groups to be compared. For example, if a researcher is interested in testing whether there is a significant difference between unpaired or independent groups for quantitative or numeric data, when there are only two groups involved in the comparison, parametric Student’s t-test is generally used if data are normally distributed. Alternatively, nonparametric Wilcoxon–Mann–Whitney rank sum test is widely applied if data are not normal. To check the normality of [Page 832]numeric data, a graphical method can be used in which the histogram of the data is compared to a normal probability curve (bell-shaped), or formal statistical tests such as the Shapiro–Wilk test and Kolmogorov–Smirnov test can be applied.

In the situation where it is of particular interest to compare numeric data from three or more independent groups, if data are normally distributed, parametric one-way analysis of variance (ANOVA) method is generally used. On the contrary, if data are not normal (e.g., scales, ranks), nonparametric Kruskal–Wallis analysis of variance of ranks, or the Kruskal–Wallis test, is used.

This entry focuses on discussing the statistical issues regarding how to compare non-normal numeric data sampled from multiple (three or more) groups using the nonparametric Kruskal–Wallis test. The remainder of the entry is organized as follows: First, a brief introduction of the Kruskal–Wallis test is provided, followed by some instructions on how to perform the Kruskal–Wallis test using various statistical software packages, including SAS, Stata, SPSS, and R. Finally, this entry concludes by clarifying a misconception about the Kruskal–Wallis test, as well as discussing the inapplicability of the method in certain settings.