Testing Hypotheses About Ordinal Interactions: Simulations and Further Comments

This paper elaborates on several issues related to testing for the presence of ordinal interactions, as described by Bobko (1986). First, the philosophy underlying Bobko's approach is explicitly stated and compared with the traditional approach to testing for the presence of interactions. Second, two modifications of Bobko's approach are described. Third, the procedures for testing ordinal interactions are compared (on the basis of Type I and Type II error rates) with each other as well as to the traditional analysis of variance (ANOVA) approach. All variants of Bobko's procedure have comparable power across different sample sizes and experimental effect sizes. These procedures differ, however, in their likelihood of falsely concluding that an ordinal pattern is present. The traditional ANOVA approach (a) is noticeably lacking in power for detecting ordinal interactions and (b) commonly identifies significant main effects but not an interaction when, in fact, an ordinal interaction is present in the population.