It is similar to the Kruskal-Wallis test in that the null hypothesis is that several independent samples are from the same population.
The test was developed by Aimable Robert Jonckheere, who was a psychologist and statistician at University College London.
The z-score equivalent is then given by In a partial replication of a study by Loftus and Palmer participants were assigned at random to one of three groups, and then shown a film of two cars crashing into each other.
[5] After viewing the film, the participants in one group were asked the following question: “About how fast were the cars going when they contacted each other?” Participants in a second group were asked, “About how fast were the cars going when they bumped into each other?” Participants in the third group were asked, “About how fast were the cars going when they smashed into each other?” Loftus and Palmer predicted that the action verb used (contacted, bumped, smashed) would influence the speed estimates in miles per hour (mph) such that action verbs implying greater energy would lead to higher estimated speeds.
[4] Jonckheere suggested breaking the ties against the alternative hypothesis and then using exact tables.
From tables with k = 3, and m = 4, the critical S value for α = 0.05 is 36 and thus the result would be declared statistically significant at this level.
, and the variance of S is then And z is given by For α = 0.05 (one-sided) the critical z value is 1.645, so again the result would be declared significant at this level.
A similar test for trend within the context of repeated measures (within-participants) designs and based on Spearman's rank correlation coefficient was developed by Page.