Multi-way Analysis of Variance

While single-factor analysis of variance only examines the influence of a categorical predictor variable on a metric dependent variable, multi-factor analysis of variance tests the influence of several categorical predictors on a metric variable. Theoretically, this can be a large number of predictor variables, but in practice and especially for Bachelor's or Master's theses, a two- or at most three-factor analysis of variance will probably make sense for reasons of sample size. An example for the application of a two-factor analysis of variance would be the question of how gender and religion affect the extent of faith. In addition to the respective (main) effects of the two factors (are there differences between genders and denominations?), an interaction between the factors can also be recorded and tested for significance (is any gender difference greater in certain religions than in others?). These interaction effects are added automatically by SPSS but especially when there are more than two categorical predictors, it hardly makes sense to include all interactions in the evaluation; rather, only interaction effects based on concrete content considerations should be included in the model.

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