Jonckheere's trend test

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 θ_i be the population median for the ith population, the null hypothesis is:

${\displaystyle H_{0}:\theta _{1}=\theta _{2}=\cdots =\theta _{k}}$

The alternative hypothesis is that the population medians have an a priori ordering e.g.:

${\displaystyle H_{A}:\theta _{1}}$ ≤ ${\displaystyle \theta _{2}}$ ≤ ${\displaystyle \cdots }$ ≤ ${\displaystyle \theta _{k}}$

with at least one strict inequality.