It would be greatly appreciated if you could kindly help me to understand how fixel-based analysis works especially in inferring significant between-group differences.

Here I have 5 questions.

**(1) Is my understanding of the statistical workflow of fixel based analysis correct?**

(step 1) smooth each fixel’s value (e.g. fiber density, fiber cross-section) based on fixel–fixel connectivity in each subject

(step 2) calculate fixel-wise t statistics by carrying out two-sample t-tests for each fixel separately, which makes an uncorrected p-value map

(step 3) enhance each fixel’s t value based on t values of connected fixels by using the equation (2) in your paper (Raffelt et al., 2015)

(step 4) permute fixel labels spatially and do the enhancement with the spatially permuted t values

(step 5) take spatially max t value for each iteration of the permutation to make the null distribution of enhanced t values

(step 6) threshold the original enhanced t map by using the null distribution (with a thresholding t value corresponding to p=0.05 based on the null distribution), which makes an FWE-corrected p-value map

**(2) In the above-mentioned step 2, what kind of t-test is used? Is that parametric two sampled t-test? Or, non-parametric t-test similar to what FSL’s randomise uses?**

**(3) In step 2, does the GLM used for the test automatically include constant term? Or, should it be included in the design matrix? Or, is there any option such as FSL’s randomise’s -D option?**

**(4) We conducted two-sample t-tests for each fixel with MATLAB (by ttest2.m function), and compared the results with figures called ‘T-values’ produced by fixelcfestats. We found that the t-maps made by MATLAB are very different from those made by fixelcfestats. Do you know what makes such a difference?**

**(5) It’s not clear to me that what kind of permutation is conducted in step 4.**

After reading your paper, we found the following description: ’ *Here, complete images are permuted as a whole, preserving the complicated dependence structure, and the maximum is computed over all fixels’ test statistics after CFE (i.e. the CFE procedure is applied to the statistic image for every permutation, effectively becoming part of the definition of the test statistic, as for TFCE or for the smoothed-variance t-map described by Nichols and Holmes, 2002).* ’ We could not find any more relevant information about the procedure corresponding to the process underlined. Could you please clarify how to make the permuted data?

Sincerely yours,

HKTH