Hi,

> I've got two groups and I want to see the correlation with a covariable as well as the differences between groups relative to their correlation. I know that I've to create 1 row of covariable for each group.
>
> My questions are:
>
> 1- If I don't need to look for mains effects (or even differences between groups of the main effect) do I need 1 other row of 1's for each group ?

Yes.  The model the mean and this is crucial.

> 2 - What the differences between these two designs ?

If you do not model the mean values then that signal will end up in the residual noise, which is incorrect and will severely hamper your sensitivity.

All the best,
        Mark

> Thank you for your help
>
> Arnaud