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I have a significant interaction $A\times B$ in my regular mixed ANOVA, but when I add a covariate, the effect $A\times B$ is no longer significant, but the interaction effect with the covariate $A\times B\times \mathrm{covariate}$ is. Why is this the case?

user48535
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    This is because the two-way interaction $A\times B$ is different across the values of $\mathrm{covariate}$ – Robert Long Mar 06 '19 at 17:00
  • Thank you. Would this be considered to be some kind of mediation effect? – user48535 Mar 06 '19 at 17:02
  • I hope not. Is $\mathrm{covariate}$ on the causal pathway from A/B to the outcome ? If so then it is a mediator and should not be included in the model if your interest is in inference. – Robert Long Mar 06 '19 at 17:05
  • No, that wouldn't make any sense. Does this kind of effect go by any specific name I could mention in the study? – user48535 Mar 06 '19 at 17:14
  • Not really, this is a fairly common occurrence with interactions. It's basically the same as a significant 2-way interaction but insignificant main effect(s). It is important to understand that the meaning of the main effect for a variable (or two-way interaction in your case) is not the same in the presence of a 2-way interaction involving that variable(or 3-way interaction in your case). There are lots of questions and answers about this here on CV, such as [this](https://stats.stackexchange.com/questions/91074/the-main-effect-will-be-non-significant-if-the-interaction-is-significant) – Robert Long Mar 06 '19 at 17:32

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