Roberto,

Before talking about R2, relative importance is tricky. Are A and B measured or manipulated? If they're measured, is it from a representative sample?

If they're both manipulated, you can argue that one manipulation has a greater main effect than the other. This can easily be tested in nested regression models, testing the constraint that both coefficients are equal. You still have the caveat that your manipulation of A may be "stronger" in some sense than your manipulation of B, rather than A being a more important predictor than B in the population.

If one or both is measured, and your sample is biased from the population in any way, relative importance can be only examined, at best, if the A and B somehow reflect the same units. Using z-scores does not help here, because the sample variance of A and the sample variance of B might be biased in different ways or to different degrees.

That said, I'm not quite sure how your last question pertains to relative importance because these are different models. Are you asking about an effect size for the interaction? If so, R2 (adjusted or otherwise) is a poor measure of effect size, and the commonly-used (especially among SPSS users) eta2 also tends to be upwardly biased. I'd look into omega2. I think that's the current best-available effect size for ANOVA models and terms.

Let me know if I've misunderstood something.

Pat

Thanks a lot Patrick.

Factor A could be two types of Diet and factor B could be with or without an additive. The assumption is that the animals treated are representative of the population. The assumption is strong but it is not the topic now.

Regarding the question, I would like a suggestion on how (and if possible) quantify the "importance" of each factor. I have proposed two models: with and without interaction.

If interaction is significant, is it still possible quantify the importance of each factor separately?

Thanks

Roberto,

Ok, got it. You can still look at omega-squared for effect size for each term, and/or constrain their effects to equality to test the difference, but with a caveat. With an interaction term, the "importance" (magnitude of effect) of A varies with the level of B. In regression terms, the coefficient for the main effect of A when there's an interaction in the model is the effect of A when B=0. So I'd suggest doing your modeling in a linear regression framework, vs. an ANOVA package, so you have full control over the parameterization of A and B and know exactly what that zero-point means.

Pat

Thanks a lot Patrick, modelling in a linear regression framework is a valuable idea. Best regards.