Hi Elizabeth,

You're raising an interesting question! Instead of weighting each individual effect based on their sample size, it's better (and makes more sense) to adopt the so-called fixed-effects meta analysis approach with which you weight each effect based on the estimate precision. The precision is the reciprocal of the estimate variance; that is, small variability means high precision of the estimate.

More specifically, if correctT.tlrc and incorrectT.tlrc are the t-statistics of effect estimate for correct.tlrc and incorrect.tlrc respectively, get the average effect with the following

3dcalc \
-a correct.tlrc \
-b incorrect.tlrc \
-c correctT.tlrc \
-d incorrectT.tlrc \
-prefix all_responses.tlrc
-expr "(b^2 * c^2 * a+ a^2 * d^2 * b) / (b^2 * c^2 + a^2 * d^2)"

Gang