Jonckheere's trend test
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In statistics, the Jonckheere trend test[1] (sometimes called the Jonckheere–Terpstra[2] test) is a test for an ordered alternative hypothesis within an independent samples (between-participants) design. It is similar to the Kruskal-Wallis test in that the null hypothesis is that several independent samples are from the same population. However, with the Kruskal–Wallis test there is no a priori ordering of the populations from which the samples are drawn. When there is an a priori ordering, the Jonckheere test has more statistical power than the Kruskal–Wallis test. The test was developed by Aimable Robert Jonckheere, who was a psychologist and statistician at University College London.
The null and alternative hypotheses can be conveniently expressed in terms of population medians for k populations (where k > 2). Letting θi be the population median for the ith population, the null hypothesis is:
The alternative hypothesis is that the population medians have an a priori ordering e.g.:
- ≤ ≤ ≤
with at least one strict inequality.