I have put a paper up on the arXiv: "Stability​ ​of​ ​Spatial​ ​Smoothness​ ​and​ ​Cluster-Size​ ​Threshold​ ​Estimates​ ​in​ ​FMRI using​ ​AFNI" http://arxiv.org/abs/1709.07471

The work therein was done in response to the paper by Karsten Mueller et al: "Commentary: Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates"
http://journal.frontiersin.org/article/10.3389/fnhum.2017.00345/full
where they carried out noise smoothness estimates using SPM12 with different resampling sizes (final voxel dimensions). They found that the smoothness estimates in SPM12 varied systematically with resampling size.

Their results made me concerned about what might happen in AFNI as a function of resampling size. My results show that the effect does occur in AFNI, but is about 4 times smaller and has the opposite sign (apparent smoothness increases in AFNI as voxel resampling size decreases).

Why does this matter? If there is a cluster of "activation", its significance is assessed by reference to the smoothness of the noise. If the smoothness estimate varies markedly with resampling size, then the significance varies markedly as well -- which is somewhat worrying, since the resampling size is a semi-arbitrary parameter. For example, if the smoothness estimate decreases as voxel resampling size decreases, then the significance of a cluster goes up as the final voxel size goes down.

Upshot: I don't think there is much to worry about this in AFNI analyses. Back to other things for me ...