Hello Donald-
We spend some time looking into this issue a year or so ago, focusing mostly on AFNI and FSL. Here are some of my notes from that time.
To see how smoothness is calculated in AFNI go to following link.
http://afni.nimh.nih.gov/pub/dist/doc/manual/AlphaSim.pdf
A good description of resels (from SPM).
http://imaging.mrc-cbu.cam.ac.uk/imaging/PrinciplesRandomFields
This is similar (but not identical) to the FSL calculation as detailed in the following link.
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0910&L=FSL&D=0&1=FSL&9=A&J=on&X=0AB9FD73CF6B45A25E&Y=amayer%40mrn.org&d=No+Match%3BMatch%3BMatches&z=4&P=256012
We found that RESELS = number of voxels and is not equivalent to an estimate of smoothness. Further confirmed by Steve Smith in this post
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0910&L=FSL&D=0&1=FSL&9=A&J=on&X=0AB9FD73CF6B45A25E&Y=amayer%40mrn.org&d=No+Match%3BMatch%3BMatches&z=4&P=251816
Also see
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0803&L=FSL&D=0&1=FSL&9=A&J=on&K=2&X=061C235962400F89F6&Y=amayer%40mrn.org&d=No+Match%3BMatch%3BMatches&z=4&P=374587
The latter lists three parameters (DLH, RESEL, FWMH) and relationship between them. Note that the results of the resel calculation are in voxels and to get the FWHM (to compare with AFNI) you would need to scale up to mm (convert units). I am less sure about this, but I think FSL assumes isotropic voxels whereas AFNI does not (smoothness calculated separately for each dimension).
Hope that helps.
In terms of your last question, I do not know about the repeated measures design. As Michael Harms and Steve Smith pointed out on a previous post to us, FSL by default uses the residuals from the second level statistical test to estimate smoothness (which assumes you did level two in FSL). AFNI recommends smoothness to be estimated on residuals from level one analyses (-errts files from 3dDeconvolve). Thus, the smoothness estmates would not change dependent on contrasts/factors based on AFNI recommendations whereas they might in FSL??? For example, looking at the main effect of Factor A versus Factor B you may have different smoothness estimates depending on the residuals from this contrast.
The FSL experts would also have to address the relationship between DOF and DLH. From memory, I think that we found that DOF changed DLH when we were playing around with the code (trying to hardcode smoothness estimates for a GRF correction rather than Monte Carlo with AlphaSim). Thus, I am also not sure how the calculations of DOF in repeated measures design would change things (as this is also different between AFNI and FSL).
Andrew
