Rajeev,
> Here's what the code does:
> In the null hypothesis, there is no true relationship
> for any given subject between his behavioural data and his fMRI data.
> In that case, we could shuffle the data across
> the different subjects, and it wouldn't make any difference.
> If we shuffle enough times, and collect all the resulting
> correlations, then we'll get the distribution of correlations
> that you would get from correlating all the fMRI scores
> with all the behavioural scores, under the null hypothesis
> that there is no true relationship between them.
The general strategy you describe for permuting is sound, but you've
left out one element: If you want to account for the multiple
comparisons problem, then you have to take the max (absolute?)
correlation, finding the max distribution, and then using the max dist
to obtain FWE-corrected P-values and thersholds. (For more on why to
use the max: http://www.sph.umich.edu/~nichols/Docs/NicholsHolmes.pdf
.) Also, since correlations have variable variance, you should use a
Fisher's Z transformation, as that will stabalize the variance. (To
see why that is important, see
http://www.sph.umich.edu/~nichols/Docs/NicholsHayasaka.pdf Fig 2)
[As you are just looking at individual correlations, you are simply
performing lots and lots of simple-correlations (simple linear
regressions). Note, that your permutation approach *won't* be valid if
you were doing a multiple regression of each ROI/voxel on a set of
predictors and wanted to look at t-tests for each predictor (an
over-all F would be OK). The problem is that one particular t-test in
multiple regression implies a null hypothesis concerning one predictor
only; the other predictors may have real effects and hence render the
data non-exchangeable, invalidiating the test. ]
However, I have to echo others' comments, that multivariate methods
might be more appropriate. Specifically, if you are interested in
finding the linear combination of your behavioral covariates that
relates to brain response (and aren't interested in identifying
specific individual covariates as significant), then multivariate
methods would be better.
Hope this helps.
-Tom
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