I did a study to look for a neural correlate to a behavioral performance score, say scoreA.
scoreA is obtained in a behavioral test. At the same time, scoreB is also obtained, though I don't care scoreB.
Six EEG indices are obtained in a design with two within-subject factors Not-Important-1 (3 levels) and Not-Important-2 (2 levels). And I am glad to find that all the six EEG indices are significantly correlated to scoreA, supporting my hypothesis.
Now I want to examine the specificity of these EEG indices as a neural correlate to scoreA. Do they only correlate to scoreA but not to scoreB? (I don't have any other behavioral measure at hand.)
A way is to calculate for each EEG index the Pearson's r between the EEG index and scoreA, as well as the Pearson's r between the EEG index and scoreB, and then use Hotelling's t-test to check whether the two Pearson's rs are significantly different. But I have a relatively small sample, so this approach is a little too conservative.
I am wondering whether it is acceptable to do a repeated measure ANCOVA. This full-factorial RMANCOVA has 2 within-subject factors as in EEG design, and 2 covariates (scoreA and scoreB). The results show a significant effect of scoreA, but no significant effect of scoreB or scoreA x scoreB interaction. All the interactions between either or both within-subject factor(s) and either or both covariate(s) are not significant. Does this support that the EEG indices correlate only to scoreA but not to scoreB?
(sadly, as scoreA and scoreB are obtained in the same behavioral test, they are not independent but significantly correlated.)