# Interaction not significant anymore in ANCOVA, but in ANOVA

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?

• This is because the two-way interaction $A\times B$ is different across the values of $\mathrm{covariate}$ – Robert Long Mar 6 at 17:00
• Thank you. Would this be considered to be some kind of mediation effect? – user48535 Mar 6 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 6 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 6 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 – Robert Long Mar 6 at 17:32