Tests for Several Independent Samples Test Types

Three tests are available to determine if several independent samples come from the same population. The Kruskal-Wallis H test, the median test, and the Jonckheere-Terpstra test all test whether several independent samples are from the same population.

The Kruskal-Wallis H test, an extension of the Mann-Whitney U test, is the nonparametric analog of one-way analysis of variance and detects differences in distribution location. The median test, which is a more general test (but not as powerful), detects distributional differences in location and shape. The Kruskal-Wallis H test and the median test assume that there is no a priori ordering of the k populations from which the samples are drawn.

When there is a natural a priori ordering (ascending or descending) of the k populations, the Jonckheere-Terpstra test is more powerful. For example, the k populations might represent k increasing temperatures. The hypothesis that different temperatures produce the same response distribution is tested against the alternative that as the temperature increases, the magnitude of the response increases. Here, the alternative hypothesis is ordered; therefore, Jonckheere-Terpstra is the most appropriate test to use. The Jonckheere-Terpstra test is available only if you have installed the Exact Tests add-on module.