Linear mixed model interaction not significant but post-hoc tests significant

Suppose I have a linear mixed model with three binary factors A, B, C.

The main effects are all significant but only the interaction A*B is significant, none of the interactions including C is significant.

I then do post-hoc pairwise t-tests with Bonferroni correction. These pairwise tests reveal that the influence of C is only significant for one out of the four possible values of (A,B). For all other values of (A,B) the post-hoc test is clearly insignificant (even without Bonferroni correction).

What does that mean?

• Any explanation for downvote? The question appears ok to me. I upvote if only to counter-balance the downvote. Commented Aug 1, 2017 at 11:49
• Thanks amoeba. I was also just wondering why the question was down voted. The question refers to a genuine problem that I have and I also checked the standard statistic literature and couldn't find an answer. Commented Aug 1, 2017 at 11:50
• FWIW, I don't think this will be answerable unless you show the summary output of your mixed model and post-hoc tests and/or post the data. Commented Aug 1, 2017 at 11:51
• fair enough, that's possible. i hoped for some general advise on how to deal with the situation of having non significant interaction term but significant post-hoc tests. or some reference to the literature. Commented Aug 1, 2017 at 11:53
• "Significant" is an arbitrary threshold, so if you have p=0.51 in one case and p=0.49 in another, there is no real inconsistency. Apart from that, different procedures have different assumptions and pairwise t-tests might not be equivalent to your mixed model analysis for various possible reasons. Showing model output and/or sharing data is the standard practice on this forum. Commented Aug 1, 2017 at 11:56