We have a doubt concerning a 2nd level analysis, whether should we stick to one-samples T-tests or if we could use a two-way ANOVA within-subjects and then do a T contrast among factor's levels. Here is a more detailed explanation, I hope it makes sense:
We have an effort task in which participants make effort either to earn different rewards (reward conditon) or not (effort only control condition). One of our interests is to compare brain signal when participants make effort to earn the reward vs effort only. Importantly, in the effort only control condition, participants were explicitly instructed to make the same effort as the previous trial of reward condition.
At first we ran the 2nd level analysis as one sample T-test using the contrast [effort reward A - effort only A] already calculated in the 1st level. So far, so good (we think).
The catch is that we are also interested in the main effect of reward conditions and the average effect of both factors. At first we built a one-way ANOVA within subjects, with 3 cells, entering each t-contrast from the 1st level [effort reward A - effort only A] , [effort reward B - effort only B] and [effort reward C - effort only C].
However, we realized that we could also use in the 2nd level a two-way (full factorial) ANOVA within subjects (independence not assumed, equal variance assumed) with two factors (type of reward: 3 levels [A, B and C] and task: 2 levels [effort only and rewarded]). With this design matrix, we could to do all the contrasts we want (the previous T-tests, average and main effect).
Obviously, the maps generated are pretty similar to the ones before, but we had a huge increase of power using this full-factorial design.
The main question is: is it acceptable by the community to use the full-factorial design for all the contrasts (T-contrasts between conditions, main effect, etc)? We believe that mathematically and statistically this is correct and equivalent, but we are are afraid that this this would be more as a 'statistical hacking', since we are increasing df and power??
Thank you very much,
Federal University of Rio de Janeiro
D'Or Institute for Research and Education