### Using Kruskal Wallis Statistic in Research

This guide will explain, step by step, how to run the Kruskal Wallis Test in SPSS statistical software with an example.

The Kruskal-Wallis test is a nonparametric (distribution-free) test, and we use it when the assumptions of one-way ANOVA are not met. Both the Kruskal-Wallis test and one-way ANOVA assess for significant differences on a continuous dependent variable by a categorical independent variable (with two or more groups).

Some people have the attitude that unless you have a large sample size and can clearly demonstrate that your data are normal, therefore, you should routinely use Kruskal–Wallis; they think it is dangerous to use one-way ANOVA, which assumes normality when you don’t know for sure that your data are normal. However, one-way ANOVA is not very sensitive to deviations from normality.

### Assumptions for the Kruskal Wallis Test

Your variables should have:

- One independent variable with two or more levels (independent groups) so the test is more commonly used when you have three or more levels. On the other hand, for two levels, consider using the Mann Whitney U Test instead.
- Ordinal scale, Ratio Scale, or Interval scale dependent variables.
- Your observations should be independent. In other words, there should be no relationship between the members in each group or between groups.
- All groups should have the same shape distributions. (Source)

### An Example for Kruskal Wallis Test

Null hypothesis:

There is no difference in the level of Happiness between marital status (single, married, divorced, widowed, and separate).

Alternative hypothesis:

There is a difference in the level.

Please watch the SPSS video Tutorial on how to run the Kruskal Wallis Test in SPSS.

Note: If you wish to take into account the ordinal nature of an independent variable and you have an ordered alternative hypothesis, consequently, you can run a** Jonckheere-Terpstra tes**t instead of the Kruskal-Wallis H test.