2x2 anova with multiple comparisons correction

AFNI Message Board
1

I am trying to run a repeat measures 2x2 anova and correct for multiple comparisons all in one, a la 3dttest++ -ClustSim. Is there any functionality to do this yet? I am using 3dANOVA3 to run the anova.

If not, which method is best for permutation testing to correct for multiple comparisons in a repeat measure 2x2 ANOVA in afni?

2

For a 2 x 2 repeated-measures design, you can break it into multiple one-sample or paired t-tests, and then run 3dttest++ multiple times.

3

How would this work in calculating F-scores?

4

For a 2 x 2 structure, the F-test for the interaction between factors A and B is essentially equivalent to the t-test (A1B1-A1B2)-(A2B1-A2B2) or (A1B1-A2B1)-(A1B2-A2B2). Even better, you get more information from the t-test than F because t-test directly provides the sign/directionality for the associated effect; for example, a positive t-value shows A1B1-A1B2 > A2B1-A2B2 and A1B1-A2B1 > A1B2-A2B2.

The same goes with the two main effects.

5

Thank you!

6

I’m sorry I don’t quite understand, actually. I am not familiar with this notation for t-tests: does (A1B1-A2B1)-(A1B2-A2B2), for example, mean I do the subtraction of A1B1-A2B1 and the subtraction A1B2-A2B2 for each subject and the run a paired sample t-test between the resultant maps? Or do I need to run ttests instead of subtractions? I’m unsure how it could be the latter, since that would only leave me with two maps for the final ttest.

I should note that all factors and levels are within subject. Every subject did all factors and all levels.

Final Q: in which of these ttests should I run multiple compairson correcting permutation tests? Running on all of them seems wrong, but so does running it on jus the final ttest.

Thanks for your help!

7

First of all, the two expressions are essentially the same thing: (A1B1-A1B2)-(A2B1-A2B2) = (A1B1-A2B1)-(A1B2-A2B2). Secondly, they are for the interaction between factors A and B in the case of a 2 x 2 design.

does (A1B1-A2B1)-(A1B2-A2B2), for example, mean I do the subtraction of A1B1-A2B1 and the subtraction
A1B2-A2B2 for each subject and the run a paired sample t-test between the resultant maps?

Yes, you can do two subtractions and then perform a paired t-test. Or, you can get (A1B1-A2B1)-(A1B2-A2B2) for each subject, and then run a one-sample t-test. The results would be the same.

in which of these ttests should I run multiple compairson correcting permutation tests? Running on all of
them seems wrong, but so does running it on jus the final ttest.

There are two aspects of multiple comparisons involved here. One is across the voxels in the brain for each statistical inference, and the other is the number of tests (interaction, main effects, and other comparisons). The first one is the major aspect everyone focuses on. There is no easy solution currently available for the second one.