Main effects as a by-product in a fixed effect 2 × 2 design, analyzed with ANOVA

摘要

To study interaction effects, two sets of data are created for fixed effect ANOVA, both with combinatory effects of the two factors. In the first, both factors and their interaction contribute independently and directly to the dependent variable. In the second, each factor contributes indirectly to the dependent score. Data created with the first model can be analyzed flawlessly. The second often show relatively large main effects and relatively small interaction effects, and as a consequence the interaction effect may be rejected. Even when the dependent variable results solely from the multiplication of both factor scores, highly significant main effects can be obtained, while the interaction effect remains insignificant. Although mathematically correct, the relative contributions of the main effects are in that case difficult to interpret.