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.
You should report both the main effects and the Interaction. Once there is a significant interaction then the main effects could be hidden or distorted due to the interaction with the second independent variable. When you graph the data, however, it should be apparent that the interaction exists and the variable that was hidden does show to functionally make a difference in the numbers dependent upon the level of the other independent variable. For example, there was a main effect of eyewitness conditions among 3 levels (No eyewitness, Credible eyewitness and Discredited eyewitness)and further post hoc testing showed those who learned of a credible eyewitness rated defendant's guilt as significantly higher when compared to either no eyewitness and when compared to discredited eyewitness was presented. No marked difference in rating of def guilt was demonstrated when the simple main effect of gender was analyzed. However, interestingly, a significant interaction suggests that men rated defendant's guilt markedly higher when no eyewitness was presented; whereas women jurors rate higher guilt if the eyewitness was discredited. Not surprisingly, men and women jurors rated equally, and leaned toward guilty, when a credible eyewitness was presented in the case.....