What can a two-way ANOVA reveal about the relationship between two independent variables and a dependent variable?

• A. It can reveal only the main effects of each variable, not interactions.
• B. It can reveal the interaction between the two variables and the main effects.
• C. It can reveal the causal direction between variables.
• D. It can replace the need for post hoc tests.

Answer: (B)

Two-way ANOVA analyzes how two independent variables influence a dependent variable, examining each variable’s overall impact and whether their effects depend on each other. It tests three things: the main effect of the first factor, the main effect of the second factor, and the interaction between the two factors. The reason this option is best is that it explicitly captures both the main effects and the interaction, which is exactly what this analysis is designed to reveal.

Understanding the interaction matters: it means the effect of one variable changes across the levels of the other variable. For instance, a treatment might improve outcomes only for one group but not another, indicating the two factors don’t operate independently. The main effects tell you whether, on average, each factor influences the dependent variable across the levels of the other factor.

Note what ANOVA doesn’t do: it doesn’t establish causal direction by itself, since causality depends on the study design rather than the analysis alone. And it doesn’t automatically eliminate the need for follow-up comparisons—if you find significant effects, post hoc or simple-effects analyses are often used to pinpoint exactly where the differences lie, especially with factors that have multiple levels.