**Re: 2X3 Anova: Interac is marg sig (p = .08) do I proceed to post hoc or increase pow**

do you mean here that Z is the usual multiplicative product of X1 and X2 or is Z just multiplying X2?

*is*X2. So what I mean is this:

lm(y ~ x1 + x1:x2)

There is disagrement on this point (note that normally you have to have two main effects to have an interaction - which I don't see in your example, but I assume is there). Some say it does not really matter if the main effects are signficant or not - don't interpret them with signficant interaction (be that regression or ANOVA). Others say that you can interpret them if the interaction is not disordinal. That is when the levels of the categorical variable don't shift their relative order, they simply are not parallel to each other at different levels of the other IV. For instance if females always have higher results on the DV than male (but the gap between them varies at different levels of another IV) you can interpret main effect despite the interaction.

Others say just do simple effects.

Others say just do simple effects.

In my view, there is simply

*no such thing*as a "main effect" (in what I view as the proper sense of the phrase) of a particular predictor when you have relaxed the assumption of additivity by including a higher-order product of that predictor. In that case, there is only the various simple effects of the predictor at different levels of either the other predictors or of itself--nothing more and nothing less. It doesn't make any difference whether the coefficient for the product is large or small, significant or nonsignificant, "ordinal" or "disordinal," etc. Now, that doesn't mean that you can't or shouldn't interpret those effects. For instance, it can still be sensible to talk about the simple effect of a predictor at the average level of another predictor, or at the average level of itself. But we shouldn't call that a "main effect" in the strict sense because the real answer to the question of "what is the predictor's effect?" is really just "it depends." Phrased as is, that is only a well-formed question if we assume that the effect of the variable is strictly additive, an assumption we have not made if we have included a higher-order product term.

Edit: Dason, I didn't have one case in mind and it doesn't matter much to me which one you want to talk about. Whichever you think is easier to explain. Or both if you're feeling ambitious.