Suppose I'm doing a 2x2 test: [A,B] x [+,-] and I want to test for difference in activations between A+ and B+ in group level to see which is stronger.

Which statistical test should I choose at the first level and at the second level?

I suppose full factorial is most flexible.

Suppose I got some activations after running both levels with full factorial,

can I just pick some of the contrasts and run second level again with a different model?

Thanks a lot in advance.

Best,

Andy