# Effect of getting closer to a normally distributed covariate on result of ANCOVA

I have a question about ANCOVA.

We did an experiment with 2 groups and then calculated an ANCOVA to see if the DV differed between the groups.

We included one binary and one continous covariate (PO). Both did not sig. differ between groups.

It was criticized that PO is skewed - we have more participants with a low PO score than those with a high PO score. It was suggested that we resample and specifically recruit those with a high PO score.

I got the tip to argue that such a change in covariate (e.g., getting closer to a normal distribution) would probably not bring major changes in the result, only smaller standard errors. However, the person did not know the exact reasoning for this anymore.

Can someone here perhaps give me a hint how I could justify this and/or literature tips on this? My research has been unsuccessful so far....

Edit: The distribution was also criticized because the group with a high PO score was relatively small - not enough in the eyes of the reviewer. I didn't make that clear before.

• AN(C)OVA, and linear models more generally, make no assumptions about the distribution of IVs (and far fewer assumptions about the distribution of DVs than is commonly assumed). I cannot think of a statistical reason to be concerned about the skew in an IV, and I would say it is incumbent on your reviewer to explain why they think their proposal makes sense. In the meantime, of course resampling will mean that your sample is not representative any more. See Miller & Chapman (2001). Aug 24, 2021 at 15:46
• The skew does not bother me. As long as you have "enough" (I'll leave that vague) members in the smaller group, you should be good.
– Dave
Aug 24, 2021 at 15:48
• Thank you for the comments! I think Dave's point is the reason why the reviewer was critical - not enough people in the smaller group. I was tol there was a statistical reason for why resampling more people in this group would probably not affect the main effect... Aug 24, 2021 at 16:18
• Where you talk about covariates you say one is 'bivariate'. Do you mean binary (taking two possible values)? Aug 24, 2021 at 16:27
• yes, sorry, binary! hooops Aug 24, 2021 at 16:54