Kruskal-Wallis H lets you decide if there is a difference in an ordinal variable e.g. user satisfaction ratings, between groups. It is the non-parametric equivalent of the ANOVA (Analysis of Variance) relying on value ranks rather than data values themselves.

Because it is based on order rather than value, the output table displayed by SOFA shows the median instead of the mean.

The p value tells you how likely the difference observed would occur if drawing from the same population (i.e. where the groups didn't really have a relationship with the value being averaged). A small p value tells you that it would be rare to observe such a difference if the group doesn't have a relationship with the value being averaged. From this we might reject the null hypothesis in favour of the alternative hypothesis - namely, that there is a difference according to the grouping variable.

In the example below (based on false data for illustration only), we shouldn't be surprised the p value is very low. It is possible to see a large difference in average age and N is reasonably large for each group. In this case we could reject the hypothesis that nation has no relationship with age.

Be aware that there is a certain sensitivity about terminology around this area. According to a widespread convention, we shouldn't conclude that there is a relationship, only that we reject the null hypothesis (see Hypothesis testing). We might go so far as to reject the null hypothesis in favour of the alternative hypothesis. See Statistical hypothesis testing.

If your data is not numeric and it is adequately normal the ANOVA (Analysis of Variance) is a good alternative.

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