Wil,
I'll just mention two simple approaches to your test:
(1) Conjunction analysis between the two -aBcontr tests can lay out all scenarios:
[
afni.nimh.nih.gov]
(2) Suppose the two fixed factors are A and B, the null hypothesis for the test you're interested is:
Ho: A1B1-A3B1=0 and A1B1-2*A2B1+A3B1=0 (*)
It is equivalent to the following null hypothesis since its second equation below is the sum of the two simultaneous linear equations in (*) divided by 2:
Ho: A1B1-A3B1=0 and A1B1-A2B1=0
Looking closely, you can see that the 2nd null hypothesis tests the main effect among the 3 levels of factor A when factor B is at level 1. With that realization, you can run 3dANOVA2 -type 3 on A1B1, A2B1, and A3B1 and the F-statistic for the main effect would be what you are looking for.
HTH,
Gang
