Testing hypotheses about ordinal interactions: simulations and further comments

Article Abstract:

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. (Reprinted by permission of the publisher.)

Statistics, Statistics (Data)

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A Monte Carlo evaluation of Bobko's ordinal interaction analysis technique

Article Abstract:

In a two-factor design, interactions are typically analyzed by analysis of variance (ANOVA). Bobko (1986) has suggested an alternative ordinal-interaction technique that might avoid spurious main effects and show more power than the classical ANOVA. In this study I (a) compared the classical and ordinal techniques in terms of Type I error rate and power under normally distributed homogeneous and heterogeneous populations, and (b) determined the effect of population non-null main effect on the ordinal technique's Type I error rate. The ordinal technique showed a substantial power superiority over the classical technique under variance homogeneity, although it did have a power cap of less than 100%. Its type I error rate under variance heterogeneity, however, was not stable and was susceptible to non-null main effects. (Reprinted by permission of the publisher.)

Monte Carlo method, Monte Carlo methods

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A solution to some dilemmas when testing hypotheses about ordinal interactions

Article Abstract:

Ordinal interactions can result in errors in traditional analyses of variance, when the interactions are based on theory. An alternative, a set of planned comparisons, eliminates these problems. This technique could help in studies on goal setting and managerial decision-making.

Psychological aspects, Methods, Goal setting, Psychology, Applied, Applied psychology

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