Additive Treatment Effects

The combined treatment

To understand the interactive effect, we need to be able to compare the effect of the combined fertilizer plus light treatment with what we expect to happen if there’s no interaction at all. Factorial ANOVA creates this no-interaction scenario by assuming that treatment effects are independent and, therefore, additive. In other words, if one treatment has an effect size of A and a second treatment has an effect size of B, then when we apply the treatments in combination, the linear -model ANOVA predicts the result to be $A + B$.

What does this mean for the analysis of this example dataset?

According to the dataset, adding light on its own increases biomass by about 30g, and adding fertilizer on its own increases biomass by 94g. So, if their effects are independent and additive, we should then expect the combined treatment to produce about 124g (30 + 94) more than the untreated control. Click “Run” in the code widget below to see how this looks: