In factorial ANOVA, what is a main effect?

In factorial ANOVA, what is a main effect?

• A. The interaction between two factors.
• B. The mean differences among the levels of one factor for factorial ANOVA.
• C. The overall mean across all groups.
• D. The variance within a group.

Answer: (B)

In factorial ANOVA, a main effect asks whether changing one factor changes the dependent variable on average, collapsing across the other factors. It looks at the mean differences across the levels of that single factor, averaged over the levels of the remaining factors. This is different from an interaction, which would indicate that the effect of one factor depends on the level of another factor. The grand mean, or overall mean across all groups, is not a main effect; it summarizes the entire dataset rather than showing how a specific factor influences the outcome. The variance within a group reflects variability inside a single cell, not differences between mean levels across a factor. For example, if you have factors like teaching method and study time, a main effect of teaching method compares average test scores across methods while averaging over study times. A main effect of study time compares average scores across different study times while averaging over teaching methods.

In factorial ANOVA, a main effect asks whether changing one factor changes the dependent variable on average, collapsing across the other factors. It looks at the mean differences across the levels of that single factor, averaged over the levels of the remaining factors. This is different from an interaction, which would indicate that the effect of one factor depends on the level of another factor. The grand mean, or overall mean across all groups, is not a main effect; it summarizes the entire dataset rather than showing how a specific factor influences the outcome. The variance within a group reflects variability inside a single cell, not differences between mean levels across a factor.

For example, if you have factors like teaching method and study time, a main effect of teaching method compares average test scores across methods while averaging over study times. A main effect of study time compares average scores across different study times while averaging over teaching methods.