> they are basically saying that t-tests should be done only for the significant
> clusters coming out of the whole brain anova F maps (it seems to me like a
> ROI approach, too)

That seems to be an opinion from what's taught in the traditional statistics books about ANOVA, but it's not something written in stone. The argument is concerned about multiple comparisons (number of t-tests) which are usually ignored in the FMRI community, and holds that you should test main effects and interactions in an ANOVA first, and then go about those individual simple (t-)tests only if the main effect or interaction is significance.

> I see in papers published by this research group that their tables show
> different p values for each significant cluster reported in the table

You mean corrected p-value, right?

> whereas in AFNI I usually report the common corrected p value obtained
> through AlphaSim. I am not sure if this is just a difference between SPM
> (with which unfortunately I am not familiar) and AFNI, which uses the
> AlphaSim approach, or if I am missing something important.

That is because the FWE correction in AFNI is done through Monte Carlo simulations in which the corrected p is estimated by counting the number of all clusters above a minimum cluster size. In the end the corrected p is associated with that minimum cluster size, and all clusters whose size is greater than the minimum carry that corrected p. If desirable, you could increase the number of simulations, and obtain a corrected p for each cluster size too, but that's usually unnecessary: as long as the corrected p corresponding to a minimum cluster size goes below a nominal value (e.g., 0.05), it does not matter how accurate each specific corrected p is.

> if the whole brain anova shows a significant interaction in the F map (eg,
> group by Task) is it ok to report this significance by picking one F and p
> value (eg, "The significant two-way interaction of Group by Task[F(2,53)=
> 3.93, p= .025] was further explored by conducting pair-wise comparisons to
> clarify significant within-group and between-group differences due to task
> condition "), and then move to t-tests results for specific contrasts?
> Or what else would I need to report? This is another point that I do not seem
> to convey clearly to the reviewers, as they think I am just doing t-tests
> without a whole brain anova.

There is some merit about the concern of multiple comparisons in ANOVA. However, some statisticians nowadays don't really care about ANOVA as experiments get more and more sophisticated. Furthermore, any F test is some kind of overall statistical test consisting of composite (multiple) effects. I would just forget about ANOVA, and go straight to those individual t-tests. The point here is, do those main effects and interactions really give you something that you can't get from those t-tests? Maybe, but that rarely happens.

So to avoid confusion and hassles from the reviewers, I would drop all the F-tests, and simply present individual t-tests in the paper.

Hope this helps,
Gang