How it works...
As we explained at the beginning of this recipe, if the interaction is not significative, Type II sum of squares are preferred. Because in our case the interaction's p-value is 0.39 > 0.05, we should use Type II sum of squares. If the interaction had been significative, we should have used Type III or I instead.
The inconsistency of Type III is reflected in the following example. If we had two effects (A,B), and an interaction (AB), Type III would compare a model with (A,B,AB) versus a model with (B,AB). This is not intuitive, why our baseline model has an interaction but not both terms of that interaction?
If we are interested in the interaction, then the distinction between Type I, II, and III is irrelevant as the sum ...
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