# CHAPTER 6Comparing More Than Two Unrelated Samples: The Kruskal–Wallis *H*-Test

## 6.1 Objectives

In this chapter, you will learn the following items.

- How to compute the Kruskal–Wallis
*H*-test.
- How to perform contrasts to compare samples.
- How to perform the Kruskal–Wallis
*H*-test and associated sample contrasts using SPSS^{®}.

## 6.2 Introduction

A professor asked her students to complete end-of-course evaluations for her Psychology 101 class. She taught four sections of the course and wants to compare the evaluation results from each section. Since the evaluations were based on a five-point rating scale, she decides to use a nonparametric procedure. Moreover, she recognizes that the four sets of evaluation results are independent or unrelated. In other words, no single score in any single class is dependent on any other score in any other class. This professor could compare her sections using the Kruskal–Wallis *H*-test.

The Kruskal–Wallis *H*-test is a nonparametric statistical procedure for comparing more than two samples that are independent or not related. The parametric equivalent to this test is the one-way analysis of variance (ANOVA).

When the Kruskal–Wallis *H*-test leads to significant results, then at least one of the samples is different from the other samples. However, the test does not identify where the difference(s) occurs. Moreover, it does not identify how many differences occur. In order to identify the particular differences between sample pairs, a researcher might use sample ...