# Definition

The** Kruskal-Wallis' H test **(named after William Kruskal and W. Allen Wallis), or One-way ANOVA on ranks is a non-parametric method for testing distributions between** independent groups of patients**. The H0 hypothesis is that all groups have the same median value, or come from the same population. When rejecting H0, we can say that at least one sample is different from the others, but without saying which one is statistically different.

Since it is a non-parametric method, the Kruskal-Wallis test does not assume a normal distribution of the residuals, unlike the analogous one-way ANOVA, and can then be used with small samples.

# In practice

The Kruskal-Wallis' H test has to be used when you want to compare distribution **between more than 2 groups**. For example, for the comparison of the size of a tumor between three cancer treatments. The groups used have to be **independent**: you can't use it to compare groups of members from the same family, groups of values from a score assessed at different times or groups of treated patients and a control group.

# How to perform a Kruskal-Wallis test?

- Go to "Test variables"
- Select a Numeric variable you would like to compare between your different groups
- Select a List variable
- Click on the panel name "Compare values of ... between groups of patients"

# The Kruskal-Wallis test is not performed

If the Kruskal-Wallis test is not performed, please ensure that:

- You have at least 3 groups in your List variable. If there are only 2 groups to compare (Yes-no variables), another test will be done according to pairing and sample size.
- Your Numeric variable has values for at least 3 patients of each group
- Your data is not normally distributed. Otherwise, an ANOVA will be performed.