On the Relationship between ANOVA Main Effects and Average Treatment Effects.

We adopt a causal inference perspective to shed light into which ANOVA type of sums of squares (SS) should be used for testing main effects and whether main effects should be considered at all in the presence of interactions. We consider balanced, proportional and nonorthogonal designs, and models with and without interactions. When the design is balanced, we show that the average treatment effect is estimated by the main effects obtained by type I, II, and III sums of squares.