Well, I just can't think of something more sophisticated right off the top of my head, but a simple case is that if you don't have any beta coefficients or contrast values available for group analysis, then converting F or t values for 3dANOVA or 3dttest might be justified.

Again, as Doug emphasized in his original message, both 3dANOVA and 3ttest assume that the input data are normally distributed. Usually this assumption is met with those beta coefficients and contrast values, but NOT necessarily true with the corresponding statistical values (this is why you need a conversion). Since you do have the beta coefficients and contrast values available, it would make sense to just use them directly instead of juggling with conversion.

Gang