# HOW TO RUN KRUSKAL WALLIS TEST IN SPSS

## What is the Kruskal Wallis Test?

### 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

• 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

The null hypothesis of the Kruskal–Wallis test is that the mean ranks of the groups are the same.
We collected data from 28 persons about their level of Happiness and marital status. We want to determine whether there is a difference in the level of Happiness (1 to 5) between single, married, divorced, widowed, and separate. Therefore, our dependent variable is Happiness (level of Happiness, 1 to 5), and the independent variable is Marital status (single, married, divorced, widowed, and separate).

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 test instead of the Kruskal-Wallis H test.

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## How to report Kruskal Wallis results: Explanation Step by Step

### How to Report Descriptive statistics Table in SPSS Output?

The first table in the output window shows descriptive statistics (number of observations, mean, standard deviation, minimum, and maximum).

### How to Report Ranks Table in SPSS Output?

The second table shows Ranks – Number of observations and Mean rank for each group.

### How to Report P-Value for Kruskal Wallis in SPSS Output?

The third table in the output window shows Test statistics. The results show the Chi-square test statistic, degrees of freedom, and p-value (Asymp. Sig.).

If p > 0.05, we fail to reject the null hypothesis.

Since in our example p = .956 > 0.05, we fail to reject the null hypothesis and conclude that there is no difference in the level of Happiness (1 to 5) between single, married, divorced, widowed, and separated.

## How to Interpret the Kruskal Wallis Test Results in APA Style?

A Kruskal-Wallis test was conducted to determine whether there is an effect of marital status on the level of Happiness. The results indicate non-significant difference, χ2(4) = .661, p = .956. We, therefore, fail to reject the null hypothesis and conclude that there is no difference in the level of Happiness (1 to 5) between single, married, divorced, widowed, and separated.

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