In factorial ANOVA, which statement describes a main effect?

In factorial ANOVA, which statement describes a main effect?

• A. The effect of one factor averaged across the levels of other factors.
• B. The interaction effect between two factors changing with levels.
• C. The overall mean across all observations.
• D. The variability within a single group.

Answer: (A)

A main effect in factorial ANOVA is the influence of one independent variable on the dependent variable averaged across the levels of the other factors. This is captured by marginal means: you compare the mean outcomes for each level of that factor while averaging over all levels of the other factors. For example, with two factors—treatment and gender—the main effect of treatment is the average outcome for the two treatment levels across both genders, and the main effect of gender is the average outcome for male and female across both treatments. An interaction occurs when the effect of one factor depends on the level of the other factor—i.e., the difference between treatment levels changes by gender. The grand mean across all observations is not a main effect, and variability within a single group is not about main effects.

A main effect in factorial ANOVA is the influence of one independent variable on the dependent variable averaged across the levels of the other factors. This is captured by marginal means: you compare the mean outcomes for each level of that factor while averaging over all levels of the other factors. For example, with two factors—treatment and gender—the main effect of treatment is the average outcome for the two treatment levels across both genders, and the main effect of gender is the average outcome for male and female across both treatments. An interaction occurs when the effect of one factor depends on the level of the other factor—i.e., the difference between treatment levels changes by gender. The grand mean across all observations is not a main effect, and variability within a single group is not about main effects.