This seems like a simple question, but I can't seem to find a clear answer, so perhaps it isn't...
Let's suppose I fit a two-way linear model with interaction term. So in R,
fullmodel <- lm(Y ~ A * B)
will give me marginal significance values for A, B and the A*B interaction. Looking at my output, I note that the interaction is significant, meaning that given that A and B are in the model, adding the interaction between them is warranted.
But I want to test the hypothesis that "B is important in predicting Y". To do this, my instinct is to use ANOVA to compare a model with B to one without.
To me, it seems logical that
modelwithoutB <- lm(Y ~ A)
and so the comparison should be
This means that I compare a model with just A to one with both a main effect of B and an A*B interaction. Do people concur? Or is there something flawed in my reasoning (or perhaps in my hypothesis)?