Unlike simpler ANOVA models, what specific test statistics does a factorial ANOVA produce for each individual main effect and interaction?

Unlike simpler ANOVA models, a factorial ANOVA produces a distinct $$F$$ ratio and $$p$$ value for each individual main effect as well as for each interaction between the independent variables.

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The factorial ANOVA is a statistical test utilized when an experiment includes more than one independent variable, such as in a factorial design. While its foundational logic is identical to that of the one-way and repeated-measures ANOVAs, a factorial ANOVA is distinct because it computes a separate $$F$$ ratio and $$p$$-value for every main effect and for every interaction effect present in the study. The specific mathematical calculations must be modified depending on whether the study utilizes a between-subjects, within-subjects, or mixed design.

Factorial ANOVA

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KPU Research Methods in Psychology - 4th American Edition

To illustrate the application of a factorial ANOVA, imagine a health psychologist investigating calorie estimation using a factorial design with two independent variables: participant major (psychology versus nutrition) and food type (cookie versus hamburger). In this scenario, running a factorial ANOVA would produce separate $$F$$ ratios and $$p$$-values for the main effect of the participant's major, the main effect of the food type, and the interaction effect between major and food type.

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