1) I would not use -detrend on the errts file - this option was intended only for use on original data for a quick look at the noise smoothness, and not for use on already processed data. However, I don't know why -detrend sometime affects the results markedly and sometimes does not.

It does not make any sense to average the 3 ACF parameters, which each represent something completely different from the others. The spatial autocorrelation function (ACF) of the FMRI noise is modeled with these 3 parameters (a,b,c) using the formula

  ACF(r) = a * exp(-r*r/(2*b*b)) + (1-a) * exp(-r/c)

where 0 < a < 1 is the weight given to the Gaussian part with st.dev. of 'b', and (1-a) is the weight given to the longer tailed single exponential part with decay distance 'c'. To see the computed FWHM of the ACF given these parameters, commands like

  ccalc 'ACFWXM(0.558,3.154,10.885,0.5)'
  ccalc 'ACFWXM(0.7097,3.1102,11.343,0.5)'

can be used, giving 8.898mm and 8.198mm (in that order). We see that the first one is slightly wider, but also has more non-Gaussian longer tail than the second one.

2) The combination of slightly wider FWHM and the longer tail in the first case (non-detrended) is what makes the cluster size thresholds somewhat higher. Note that these cluster size thresholds differ more markedly at the larger p-value thresholds, which is due to the longer single exponential tail. At the smaller p thresholds (say p=0.002), the cluster thresholds aren't that different (14 and 11 voxels).

3) Generally, in a group study, we recommend taking the (a,b,c) values from each subject and averaging them to get a group set of (a,b,c) values, and THEN using those in 3dClustSim. This method is ad hoc, but works OK. I would not apply '-detrend' to errts.* datasets.

4) Do you have an updated copy of AFNI binaries? I made changes to ETAC in September/October and would now recommend the use of the default "global ETAC" method, rather than the previous "local ETAC" method. If your "afni -ver" indicates a date earlier than (say) 15 Oct 2018, please update your AFNI binaries and try running 3dttest++ -ETAC again. However, it looks like you have the global ETAC output file TT.c7xJqG0BM99.robin.ETACmask.global.1pos.5perc.nii.gz which is a binary mask of all voxels that passed the ETAC multi-testing method (1pos means a 1-sided t-test, on the positive side; 5perc means at the 5% global statistical significance level). The multi-level cluster-thresholds used are in the globalETAC.mthresh.*.niml files (XML formatted, but readable text).

4a) You can think of cluster-size as

   sum              z(v)^0
   {v in cluster}

where z(v) = z-statistic (converted from t-statistic) and z(v)^0 is z(v) raised to the 0 power -- that is, 1. Now replace the exponent '0' with 'hpow'. This is a generalization of cluster-size that gives more weight to more statistically significant voxels. Since the voxel p-value threshold is also a threshold on the voxel z-value, there is a floor value to z(v) in a cluster - so all voxels will count in this sum, but with hpow > 0, some voxels are more equal than others.