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We are running a 2-way anova.

We found that one of the IV has a significant main effect. The second IV does not have a significant main effect. However, post hoc tests do show significant effects between some of the levels within the second IV.

I was under the impression that, if there is no significant main effect for an IV, one should not perform post hoc tests, as they would then be unreliable. Is this true?

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Yes, it is unreliable. Post-hoc tests shouldn't be performed if the ANOVA is not significant. You're most likely getting a statistical fluctuation due to multiple comparisons issues. I'm ready to guess that your "significance" of the post-hoc test is very borderline.

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  • $\begingroup$ In one case p < .00001, in another case it is indeed very borderline. Would the first be acceptable, while the second is off? Do you have any source for this so I can look into it more? $\endgroup$ Mar 2 '20 at 15:04

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