Test for interaction between treatment and stratum with ordinal responses

A measure of interaction between treatments and stratum is proposed when there are two treatments and the response variable is measured on an ordered categorical scale. A test of the hypothesis of no interaction and a test of the hypothesis of no treatment effect are given and approximate expressions for the powers of these tests are obtained. Monte Carlo simulation is performed to examine the Type I error rate and the accuracy of the approximate power formulae of the tests. The loss of power of the tests due to combining categories is also examined. The simulation study shows that our methods perform well even in samples of size 20, and that the dichotomization results in appreciable loss of power.