A researcher runs a 2 (Diet: Low-carb vs Low-fat) × 3 (Exercise: None, Moderate, High) two-way ANOVA predicting weight loss. The interaction Diet × Exercise is significant (p = .02). The researcher asks: “Should I run Tukey post-hocs on the Exercise main effect to compare None vs Moderate vs High?” What is the best statistical advice?
Yes—if the interaction is significant, you should always interpret the main effects first and then do Tukey on the main effects.
No—when the interaction is significant, you should focus on simple effects (e.g., compare Exercise levels within each Diet group) with appropriate multiple-comparison control.
Yes—because post-hoc tests are only for two-way ANOVA, not one-way ANOVA.
No—post-hoc tests are never appropriate in factorial ANOVA designs.