ANOVA: do I interpret the significant main effects not involved in interactions? My statistical model is Dependent ~ A * Sex + B * Sex. (i.e., Dependent ~ A + B + A:Sex + B:Sex). I have prior reason to expect that Sex will interact significantly with A and B, but no reason to expect that A and B will interact. When I run my data, I get these results.


*

*A (significant main effect) 

*B (not significant) 

*A:Sex (not significant)

*B:Sex (significant interaction)


That is, there is a significant main effect of A, and an interaction between B and Sex. My understanding of ANOVA is that since B:Sex is significant, I need to segregate the data by the levels of one of the factors (I will choose Sex) and test the effect of B on each subset separately. But, should I interpret the main effect of A before doing that? Or should I segregate the data, and retain the independent variables A and B in the test for each subset?
 A: It is unclear from your question whether you are still engaged in model selection, or whether you have settled on your model and are now only interested in interpretation of the outcome.  In view of the description, I am going to assume that you are still undertaking model selection, and you are interested in comparing the present model with one that removes the interaction of A and Sex.
In these kinds of models it is generally a bad idea to monkey with the data to try to segregate it.  It is much simpler just to fit the two nested models of interest and then use a standard goodness-of-fit test comparing the nested models to see if there is any evidence to include the extra parameters in the larger model.  In your case, the comparison of interest is between these nested models:
Model 1:  Dependent ~ A + B + Sex + A:Sex + B:Sex
Model 2:  Dependent ~ A + B + Sex + B:Sex
It should not be difficult to calculate the goodness-of-fit statistics for these two models and then perform a comparison, noting that Model 2 is nested within Model 1.  This would usually be done with a chi-squared test comparing the log-deviance of the models.
