> Also, since correlations have variable variance, you should use a Fisher's Z transformation, as that will stabalize the
> variance.
Hi Tom, what about covariances? Do covariances have variable variance? (I recently needed to do permutation tests on something
more like covariances rather than correlations.)
Thanks,
joe
----- Original Message -----
From: "Thomas E. Nichols" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Friday, April 21, 2006 11:37 AM
Subject: Re: [SPM] Q: Permutation test for non-spatial multiple-comparisons correction?
> 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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