When reporting a two way 2 x 3 mixed ANOVA I have recently heard that the interaction effect should only be reported if the two main effects are significant (APA style). Is this correct?
If you report the interaction, you need to report the main effects as well, whether pooled (as @Frank suggests) or "plain". I usually report some predicted values as well - often in a graph - as I think these show things intuitively.
I agree with @Frank about significance tests. That's not a good way to build a model.
I think you may have mis-remembered the advice. It is true that you should not interpret main effects in the usual way when there is an interaction. And I've heard some people say that you should not report an interaction if it is not significant, although I don't agree.
Usually "significance" should not determine what is reported. I would always report the interaction tests and the pooled interaction + main effect tests, which have an easy interpretation independent of data coding. Main effect tests are not generally of interest when interactions are in the model, and they are at the whim of coding choice. The R
rms package makes this easy to do even when not assuming linearity of effects.
No not correct (where did you hear this from and what does APA style have to do with anything?).
If the interaction is significant then it is the most important effect to interpret, regardless of whether or not the main effects are significant.
Edit: The question has been edited to reporting the interaction instead of investigating, my answer refers to investigating.