Thanks for the quick reply! I have some questions though:
> The advantage of the F-test would only apply if you used a more advanced correction for multiple comparisons than the
> standard divide by N tests.
Not sure what you mean: When conducting the F-test or during the post-hoc tests?
> Also, you can't limit your search region to only areas with a significant F-test because that would be considered double
> dipping.
Why not? E.g. take a neuropsychological test battery with 20 individual tests and three groups A, B, C. I would run post-hoc tests A vs. B, B vs. C, A vs. C for those neuropsychological tests only that showed a significant group effect?
> For these reasons, people seem not to correct for the number of multiple comparisons.
But then it should be more conservative to run an F-test and limit any further post-hoc tests (uncorrected or corrected for multiple comparisons), to areas that already showed an effect? BTW, it also seems to be standard to conduct two one-sided t-tests A > B and B > A with e.g. p = .001 instead of using a corrected p = .0005.
Leaving this aside, if I plan to run t-tests anyway, then there would be no reason to build a second-level ANOVA, or is there any? With "t-tests" inside a purely within-subject "Flexible factorial" model the effects seem to be (much) larger compared to a one sample t-test based on the corresponding con images generated on single-subject level. Or would the results of the "Flexible factorial" be correct?
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