The difference between the Kruskal-Wallis test, the Friedman test, and the Jonckheere-Terpstra test

The Jonckheere-Terpstra, Kruskal-Wallis, and Friedman tests are all non-parametric statistical tests that are used to compare multiple groups of data. However, there are some differences between these tests, and their appropriate use depends on the type of data and research question being investigated.

TL;DR The Kruskal-Wallis and Friedman tests are used when the groups are independent and related, respectively, and the dependent variable is continuous but not normally distributed. The Jonckheere-Terpstra test, on the other hand, is used to test for trends in ordinal independent variables with a continuous dependent variable.

The Kruskal-Wallis test

The Kruskal-Wallis test is used when there are three or more independent groups and the dependent variable is continuous, but the data is not normally distributed. It tests whether the median values of the groups are significantly different from each other. The Kruskal-Wallis test is an extension of the Mann-Whitney U test, which is used to compare two independent groups.

The Friedman test

The Friedman test is used when there are three or more related groups and the dependent variable is continuous, but the data is not normally distributed. It tests whether there are significant differences between the medians of the groups, taking into account the dependence between the groups. The Friedman test is a non-parametric alternative to the repeated-measures ANOVA test.

The Jonckheere-Terpstra test

The Jonckheere-Terpstra test is used to test whether there is a significant trend in the data between an ordinal independent variable and a continuous dependent variable. It is often used when the groups are ordered, such as when comparing different dosages of a medication or different levels of a disease severity.