# 2x3 ANOVA interaction no longer significant after including a covariate? [duplicate]

My experiment had a 2x3 design with one covariate. If I analyse the results using an ANOVA, I get a strongly significant interaction between the two main factors (p<.001). If I add the covariate into the analysis and do an ANCOVA, the interaction between the two main factors is not significant (p=.252).

The covariate itself was not significant, nor did it have any significant interactions.

There are similar questions on this website, but I was hoping to understand what does such a result pattern say about the covariate? How should I interpret the results?

Adding the covariate was the novel feature of my study and therefore it is important to me to understand this interaction properly.

Is the covariate influencing the results?

EDIT:

I've been thinking about this all day and I guess the possible interpretation would be: When controlling for the covariate, the interaction of the main effects is no longer significant.

In which case I don't understand a couple of things:

a) Does that mean the covariate is responsible for the interaction?

b) Why is the interaction between FactorA*FactorB*Covariate not significant then?

c) Why isn't the covariate significantly interacting with anything at all, when its presence seems to be influencing the results?

EDIT 2:

Maybe I am doing something wrong, because it is not making much sense to me. Here are my results:

http://imageshack.us/g/580/ancova1.png/

The last two pictures show when I run an ANOVA without the covariate (repeated measures, Factor 1 (2 levels). Factor 2 (3 levels).

The first three when I run an ANCOVA on the same factors, except I put in OptimismScore as a covariate.

## marked as duplicate by kjetil b halvorsen, mdewey, Michael Chernick, Peter Flom♦Jul 4 '18 at 19:24

• What happens if you run the same model, with the covariate as the outcome? – Jeremy Miles Apr 29 '13 at 17:18
• The covariate itself is not significant (p=.622) – Tomas Engelthaler Apr 29 '13 at 18:44
• Think of this: suppose the covariate were practically equal to the interaction. Then, upon introducing the covariate, there would be no need for the interaction at all. – whuber Apr 29 '13 at 19:40
• Interaction terms are sometimes correlated with omitted main effects. I think it's best to get the main effects right before looking at interactions. – Frank Harrell Jul 29 '13 at 12:18
• If you did it correctly, centering should have no effect on interaction term estimates and their standard errors. Centering should only affect main effects. – Frank Harrell Jul 29 '13 at 14:57