## Wednesday, May 4, 2016

### Multiple Comparisons : Kruskal Wallis Test

Keeping with the theme of my last three blog posts, I wanted to continue on with the idea of explaining multiple comparison tests that are available to us for statistical analysis.  This post will focus on the Kruskal WallisTest. Emily Summerbell also posted a great entry (HERE) about this same test and walks through how to perform this test on Prism, but I want to focus more on understanding the why of it, rather than an example.
The KruskalWallis H test is otherwise referred to as the One way ANOVA test on assigned ranks. It is simply a test that can be used determine whether a significant difference exists between two or more groups of an independent variable on a continuous or ordinal dependent variable set, and analyzes rank based, nonparametric data sets.  As mentioned, the Kruskal Wallis test is the ANOVA alternative for nonparametric data sets and is an additional extension of another statistical test we’ve encountered in this class, the Mann Whitney U test.
As a quick refresher for those that have forgotten, the Mann Whitney U test (also called the Mann Whitney Wilcoxon test, or the Wilcoxon rank sum test) is a nonparametric test of the null hypothesis that is used to determine if two samples came from the same population, and/or that the value from one particular population may tend towards a larger value than the other. In comparison to the Student’s T test, Mann Whitney tests are not under the assumption of a normal distribution of the populations, but still functions with similar efficiency. The one difference between the Mann Whitney test and the Student’s T test is that the Mann Whitney test has a reduced ability to indicate significance because of outliers.
A few assumptions that come with the Kruskal Wallis test are:
1.     Your dependent variable should be ordinal or continuous
2.     Your independent variable should consist of two or more categorical groups that are independent of each other.
3.     All of your observations should be independent of each other.
4.     The shape of your population distributions needs to be determined in order to know what your Kruskal Wallis test will compare. If the distributions for your independent sets are of the same shape, you compare medians of the dependent variable; if they are of different shapes then you compare means.
One important key feature of the Kruskal Wallis H test is that is not a post hoc analysis test, and that it does not tell you which specific groups in your independent variable set are statistically significantly different, but rather it tells you that there are at least two groups of your independent variable that are different.

As a quick side-note, there is a repeated measures equivalent for nonparametric data, called the Friedman’s test.