> The average cost value is significantly different between groups. So this means I need to add
> -center DIFF to my 3dttest++ script correct? How does this change the interpretation?

There are usually two research goals with a situation yours:

1) examine and compare the two groups while controlling for the covariate;
2) examine the correlation between BOLD response and the covariate (and sometimes compare the correlation between the groups).

If 2) is your ONLY goal, the centering issue is irrelevant and you can center whatever you prefer. And your initial question can be clarified:

> Positive correlation for sub-brick[2] (the behavioral covariate effect)= a higher behavioral value is correlated with more volume in the individual.
> Negative correlation for sub-brick[2] (the behavioral covariate effect)= a lower behavioral value is correlated with less volume in the individual.

-- At sub-brick #2 'old-young_cost' datum type is float: -1.9144 to 2.6131

It basically shows that the old group has higher correlation between the young group. The word 'higher' does not say anything about the sign (positive or negative) of the correlation. However, they can be found in the following sub-bricks:

Correlation for the old group:

-- At sub-brick #6 'old_cost' datum type is float: -1.52621 to 1.71339
-- At sub-brick #7 'old_cost_Tstat' datum type is float: -4.8015 to 5.5645

Correlation for the young group:

-- At sub-brick #10 'young_cost' datum type is float: -2.08607 to 1.47662
-- At sub-brick #11 'young_cost_Tstat' datum type is float: -6.61598 to 6.92221


However, if 1) is of interest, things become very subtle and difficult when the average covariate value is significantly different across groups.

Gang