Monotonic hypotheses in multiple group designs: A Monte Carlo study.

Monotonic hypotheses are predictions about the ordering of group population means. A journal survey revealed that the problem was very common and that there was little uniformity among researchers regarding the statistical test to use. Most of the approaches in the literature to detect both monotonic trend and nonmonotonicity were compared under varying population conditions in a Monte Carlo simulation. The results suggested that only rarely will sample means order the same as the corresponding population means, leaving the approaches most researchers used with far too little power. Trend tests had far greater power; the one recommended is the familiar linear trend test. However, used alone this test does not detect the presence of any instances of nonmonotonicity. Therefore, it should be used in combination with a technique that can detect such inversions, preferably the Sidák-corrected reversal test conducted with a very high α (.50). (PsycINFO Database Record (c) 2010 APA, all rights reserved)