I did a 3x2 anova - my data looks like in the figure belowenter image description here

I get significant main effects and a significant (3x2) interaction.

I now want to test the interaction between the blue and green bars. So something like a post-hoc 2x2 anova. This sounds weird though. So I have two (I think) simple questions:

  1. How should I report it? I have good reasons to test the 2x2 interaction, but I can't really call it a planned comparison: it's not quite theory-driven.

  2. Should I do any corrections? It would make no sense to test all possible interactions, but I could have also tested the interaction between red-green and red-blue. Should I then correct my critical values accordingly?

  • $\begingroup$ Since you don't have any a priori hypotheses, I would run a Tukey HSD test for both main effects and the interaction effect. Then look at the output and report only those comparisons you are interested in. $\endgroup$ – Stefan Dec 17 '15 at 16:58
  • $\begingroup$ Thanks, but I'm interested in the 2x2 interaction, not in a simple comparison of means. I guess it wouldn't be appropriate to correct the F value with Tukey's correction, right? $\endgroup$ – elisa Dec 18 '15 at 10:09
  • $\begingroup$ OK, I don't really know where to start but your are confusing a lot of terms here. Pretty much everything in ANOVA is about comparing means, incl. post-hoc tests, which are done after the ANOVA and when no a priori hypotheses were specified.The F-value is simply the signal to noise ratio - why would you want to adjust this? Have a look what having an interaction means. $\endgroup$ – Stefan Dec 18 '15 at 15:30
  • $\begingroup$ Thanks. Sorry, I didn't explain myself well. I think we're just talking past each other. I'm not as lost as it may sound, I think it's pretty clear to me what an interaction is. I'll try to rephrase the question. $\endgroup$ – elisa Dec 19 '15 at 9:45

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