# Why is ANOVA interaction no longer significant after including a covariate?

I have initially run a 2x2x2 Anova and found some significant interaction between the independent variables. I then ran a ANCOVA where I added a covariate. I am confused with how to interpret the output from the ANCOVA as the significant interactions that I found with the ANOVA are now insignificant in the ANCOVA.

• This means that, after controlling for the covariate (that is, holding it constant) the other independent variables are no longer significant. – Peter Flom Apr 27 '13 at 13:39

First, the difference between significant and non-significant is not necessarily significant. So if after adding a covariate your interaction p-value changed from .04 to .06, this doesn't mean anything substantial other than you've bounced from one side of a binary .05 decision threshold.

However, the other possibility is that the covariate has substantially influenced the analysis. A typical motivation for including a covariate is that you want to control for its effect, and thereby adjust your estimates of main and interaction effects for the covariate.

I recommend that you produce a few plots of the cell mean both controlling and not controlling for the covariate to see what kind of difference inclusion of the covariates has made.

• Thank you for the pointers. Looking at the means and plots there is a large difference between the ANOVA and the ANCOVA. I'd understand it if the ANOVA wasn't significant and the ANCOVA was, obviously the covarient would be having an effect on the scores. But I can;t wrap my head around what it means to have gone the other way, can this still mean the covarient is having an effect? – liz Apr 27 '13 at 19:57
• A standard scenario is that groups differ on the covariate. Thus, once you adjust for baseline differences between groups on the covariate there are no longer group differences. Things are more complex when it comes to interactions, but the same idea holds. – Jeromy Anglim May 2 '13 at 11:08