# Assumptions for repeated measures ANOVA with covariates

Hey all

I am running a one way RMANOVA with independent variable (pair type) and two covarites (T_Sc_Diff, N_Items_Diff).

I know that in ANCOVA a main assumption is that the interaction between the IV and the covariate be non significant, does this hold in RMANOVA too?

Put simply should I be worried that the "within subject" interaction of PairType* T_Sc_Diff is signifcant (Yellow box) or is should I be looking at the "between subject" where T_Sc is non significant (green box)

Thanks

Yoni

## Comments

Dear Yoni,

These are some deep questions :-) First off, my current thinking is that it is statistically allowed to add covariates that correlate with the grouping variable (it is as if you are adding a factor to a regression model), as long you realize this complicates the interpretation of the outcome. My thinking on this is still in flux though.

Now I would not include a covariate that does not do anything -- this just adds noise and complicates your model needlessly. And I think you are in that situation: T_Sc_Diff does not seem to add much. So I would just leave it out. Now if it

hadbeen a relevant covariate, then it would have been problematic (in terms of the interpretation) if there was this interaction with the grouping variable.Cheers,

E.J.

Thanks for the response!

I still want to include the covariate T_Sc_Diff because of its theoretical importance (namely it could be an alternative explanation).

What I want to show is that the main effect of PairType is significant (and explains a larger proportion of variance then T_Sc_Diff). Doesn't the first line of the output support this claim? Or in other words why does the interaction complicate interpretation? And finally, how would you report this?

Needless to say the equivalent Bayesian model supports the Pair type main effect very strongly over all alternative models, but I'm still looking to report the frequentist statistics in addition to the Bayesian...

Thanks again

Y

Hi Yoni,

A quick note from my holiday destination: Miller and Chapman (2011) is a recent reference on why the interaction complicates the interpretation. The latest edition of the textbook by Andy Field also discusses this.

Cheers,

E.J.