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I ran a 2 (factor A: A1 vs. A2) X 2 (factor B: B1 vs. B2) between-subjects design experiment.

I had an a priori prediction that the effect of factor B (i.e. the difference between B1 vs. B2) would NOT be significant in condition A1 but WILL be significant in condition A2

When I run an ANOVA, the interaction effect is not significant, but the a prior predictions are supported when running contrast analyses (or simple effects analyses)

Is it okay to report something along the lines of "although the interaction effect was not significant (XXXX), contrast analyses revealed that the difference within A1 was non-significant (XXX), while the difference within A2 was significant (XXX)"? Or can I say nothing about the contrast analyses because the interaction effect was not significant?

I think I heard a professor at a conference say that as long as you had a priori hypotheses this should be okay

If anyone has references for anything relevant that would also be greatly appreciated!

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  • $\begingroup$ What is an a priori prediction? $\endgroup$
    – user2974951
    Commented Jul 18, 2019 at 9:50
  • $\begingroup$ I meant that we had specific predictions regarding the difference within condition A1 and condition A2 before running the experiment $\endgroup$
    – PRS_CU24
    Commented Jul 19, 2019 at 1:10
  • $\begingroup$ I don't understand. Can you give more context about what it is that you are doing, what is the goal, and the experimental setup. $\endgroup$
    – user2974951
    Commented Jul 22, 2019 at 6:07
  • $\begingroup$ Sure! For simplicity, let's say I'm trying to show that females (a2) enjoy rock music (b1) more than classical music (b2), but males (a1) enjoy them the same. I run a 2 x 2 between-subjects design study and find that the interaction effect is not significant. However, planned contrasts reveal that females actually do enjoy rock music more than classical music, whereas males enjoy them the same. In this case, is it possible for me to claim that females enjoy rock more than classical music, while males like them the same, even when the interaction effect is non-significant? $\endgroup$
    – PRS_CU24
    Commented Jul 24, 2019 at 3:50

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