Dear Rick, Gang,

Greetings AFNI land! Long time watcher, first time poster.

With Anders Eklund, I'm doing some evaluations of cluster size inference with group analysis. We've talked about this issue and I'm worried there might be problems with the approach of estimating group-level error smoothness with first-level residuals.

First, I think Rick is suggesting there's only a single volume to estimate smoothness from; that's not the case, as you have nSubject residuals at the group level from which to estimate smoothness. (I realise that residuals are not saved by 3dttest++, but 3dMEMA does and, for a one-sample t-test you can just de-mean with 3dCalc or 3dDetrend to get residuals.)

Second, the variance at the 2nd level has contributions from both the intra- and between-subject variance, and hence the smoothness does too. To fix notation, let sigma^2 be the average intrasubject variance, and tau^2 be the intersubject variance; and let mu be the group-level mean. Now, it is true that if there was no group effect (the case under the null) then we'd expect intra-subject variance sigma^2 to dominate, but the group level null hypothesis is only on the mean; i.e. we're testing H0: mu=0, not H0: mu=0, tau^2=0. But when we estimate the smoothness from 1st level only, it seems to imply a group level null of H0: mu=0, tau^2=0, which has a fixed effects feel to it.

Finally, SPM estimates smoothness from the group level residuals and generally gets sensible smoothness estimates. They are justified in part by an old paper of J-B Poline's [1], which found that the uncertainty in smoothness estimation resulted in sampling variability in corrected P-values of about 10% *when* smoothness is estimated from a single image (the observed statistic image, as was done at the time). Thus, when multiple (residual) images are used there should be yet less variability in the smoothness estimate.

Anyway! Interested what you think of these arguments, and maybe this is also a feature request to add residual output to 3dttest++.

-Tom


1. Poline J-B, Worsley KJ, Holmes AP, Frackowiak RSJ, Friston KJ. Estimating smoothness in statistical parametric maps: variability of p values. J. Comput. Assist. Tomogr. 1995;19(5):788–796.

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> To Gang's response I might add that estimating the
> smoothness of the noise from a single volume (and
> via division no less) is itself a very noisy computation.
>
> Estimating the smoothness of the noise from the EPI
> time series does it from hundreds of TRs (and times
> the number of subjects), so the estimate should be
> far more robust. And since both estimates are
> attempting to estimate some sort of larger voxel size
> based on that smoothness, it seems fair to think that
> both methods are trying to estimate the same thing,
> particularly from the viewpoint of Monte Carlo simulations..
>
> - rick