Hi, Anderson

Thank you so much for very detailed and easy-to-read explanation.One further question is the popular TFCE method, which seems to make a transformation of raw statistic map by incorporating both its height (how high the statistic of a voxel is) and extent (Is this voxel in a cluster) information. The transformed maps (i.e., TFCE maps) go through a permutation test to obtain corrected p-values. Therefore, TFCE method is a voxel-based (instead of cluster-based) correction method but considering the spatial cluster information, in comparison with the original voxel-based method. Is my understanding right? Thanks!

Best,

Yang Hu

在 2019-02-25 20:19:42，"Anderson M. Winkler" <[log in to unmask]> 写道：

Hi Yang Hu,

Please see below:

On Sun, 24 Feb 2019 at 05:01, huyang <[log in to unmask]> wrote:

Dear FSL experts and users,

(1) Suppose that I collected two groups of data and computed the voxel-wise metrics (for instance, gray matter volume). I would like to test the hypothesis that whether the two groups differ in some brain regions. I could get a voxel-wise P-value map by conducting a Two-sample T-test in each voxel independently or by conducting a permuation test in each voxel independently. This is the difference between parametric and non-parametric hypothesis testing, I think.

In both cases you'd do a two-sample t-test. In the parametric you'd use a formula that is based on some assumptions or knowledge about the data to obtain p-values. In the permutation case, you'd shuffle the group membership so as to obtain a permutation-based p-value.

 

My question is that when using FSL's randomise, permutation test is used for calculating raw P-values?

Yes.

 

(2) After I get a voxel-wise P-value (T-statistic) map, I need to correct these P-values for multiple comparisons.

One way to see this is, as you say, need to correct the p-values. Another way to see this is that you need to obtain p-values that take into account the multiplicity of the tests, even if the uncorrected p-values had not even been computed. For both RFT and permutation testing, one does not, in fact, need to ever compute the uncorrected, "raw" p-values, and it's possible to proceed straight to the FWER-adjusted p-values.

 

Random field theory could be used to estimate the P-value threshold at a FWER of 0.05 (voxel-based) or cluster size threshold at a FWER of 0.05 (cluster-based).

Yes. Note that cluster-level statistics are not a form of correction. Rather, they are statistics on their own right, for which both uncorrected and corrected p-values can be computed (it turns out that, for cluster, uncorrected p-values seldom make any sense, because clusters move around, so we always think about corrected p-values in that case).

 

FSL's randomise could also be used for voxel-based/cluster-based thresholding. My question is that how could permutation be used for multiple comparison correction? Is it based on the maximal statistic (the maximum of a statistic map) distribution during the permutations?

Yes. For the test statistic obtained at each voxel, the FWER p-value is computed by considering the distribution of the maximum statistic across the image.

All the best,

Anderson

 

I read the related papers but these are too technical (difficult) for me, and I would like to have a basic but not-too-wrong conception. Many thanks.

 

Best,

Yang Hu

 

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