Firstly, remember that when you fit interactions, the main effects are very difficult to interpret. So in this model I won't do any contrasts involving the first three columns.
Second, as I've droned on about before, over-all de-meaning of covariates is usually only important when fitting fMRI data, or any sort of differenced data. As you're modelling (positive) FA data, this isn't so much of a issue here (you can or cannot demean the entire covariate, and results will be the same either way). Likewise, because of Gr{A,B,C} modelling the main effect of group, centering a covariate within each group is done automatically and doesn't need to be done explicitly.
If this is right are the following contrasts and my interpretations correct:
0 0 0 1 -1 0 0 0 0 = where is the correlation between data in Gp A and X
bigger than the correlation between data in Gp B and X, whilst allowing for
any effect age may have on data and X within each group
Yup.
0 0 0 1 0 0 0 0 0 = where is there a positive correlation between data in Gp
A and X whilst allowing for the effect age may have on data and X within Gp A.
Yup.
If this is correct:
1) Adding any other confounding variables within groups would involve again
splitting then into three groups and demeaning in each group before padding
with 0s ?
Yes, but, again, demeaning is not needed.
2) As this design gets bigger, is it better to analyse using a single large
group like this or would it be better to split into 2 analyses one with Gp A
and B and another with Gp A and C (where A is control group)
Depends on the question. The more different factors/questions you add into a model, the bigger assumptions you make. Even with the non-parametric randomise, you are making a homogeneity assumption... under the null hypothesis, after discounting any nuisance factors, the distribution of the data is the same in every group modelled. The smaller the model, the smaller the scope of this homogeneity assupmtion. The only flip side relates to the variance and permutations; variance can be difficult to estimate with few subjects (less than 20, especially less than 10) and so considering a larger model with more observations to contribute to a variance estimate can help; likewise, if you have a tiny amount of data you may not get enough permutations to have a reasonable test, and again you might be served better by a bigger model.
3) If one did not split age into 3 groups but included it as a single Ev
across all 3 groups and applied a similar contrast to the above what would
be the interpretation of this or would it be nonesensical ?
Good point. It is simply a question of whether you believe you need a group-by-covariate interaction. I.e. for each covariate, consider if you need to let it vary by group. If it is not a reasonable concern that it could be different in each group, then you can include the covariate as a single regressor and don't worry about the covariate-by-group interaction.
