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Re: Multi-masking for Multiple Comparison Correction

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Fri, 3 Oct 2008 18:21:27 +0200

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 ```Independence is a concept applicable to random variables. In the frequentist approach, violations of the null hypothesis are fixed (not random). In the example you make, the null hypothesis is violated by the angry faces condition, but the errors are still random. The test statistics in question remain independent assuming normality of the errors. If the normality assumption is violated, the test statistics are only uncorrelated. As a first reaction, I'd say that the problem in the example you present is not where you think it is. The ANOVA assumption is that your fixed effects sum to 0, so you will not be able with your ANOVA model and your contrast to determine that it's only angry faces that drive the association, only that the angry - happy difference is positively associated with the signal. But say you'd included neutral faces. Then you could use pairwise comparisons, and I see no problem with the case you mention where you find that only angry faces differ from neutral. But notice the conditionality on the first contrast: your design includes only two types of faces, this larger design three, so that the set of voxels examined in the second contrast may be different. - Roberto > The condition of orthogonality seems to me not entirely clear. Is it > the contrast vectors that need to be orthorgonal, or the contrast > estimates themselves? e.g. In my example of a face and dot > presentation task, my functional ROI might be determined using: > > angry faces: 0.5 > happy faces: 0.5 > dots: -1 > > whereas my final contrast of interest is: > > angry faces: 1 > happy faces: -1 > dots: 0 > > These two contrast vectors are orthogonal. But if the first contrast > is driven exclusively by angry faces producing high activation and > dots and faces producing little activation, is the ROI defined on that > basis truly orthogonal to the contrast being tested? Because in the > extreme case, it would seem to collapse to the situation in which the > mask used to restrict the search space wholly corresponds to the > contrast being tested. Would a more appropriate approach using my > example be to define a functional ROI based on a conjunction of > angry-dots and happy-dots contrasts? > > -Tom > ```