I would use the text you e-mailed as a footnote and just cite similar studies in the literature that used the same number (or less) of subjects you intend to use and were able to show significant results. This should be sufficient. It would be useful to cite the material below as archived on the SPM Helpline - but I am not sure it was posted. I am therefore posting this to the help line for comments and for you to be able to cite it, if you want.
I hope this helps :) - Karl
From: Viding, Essi
Sent: 04 November 2011 00:50
To: Friston, Karl
Subject: power question
Dear Professor Friston,
The following text has been used by an ICN colleague who has quoted you in his previous grant application (s?)-
>> There is no principled power analysis that can be applied in
>> the context of classical inference using the topological
>> mass-univariate approach adopted by the standard analysis approaches
>> using Statistical Parametric Mapping. This is because specification of
>> the alternate hypothesis is not possible in quantitative terms
>> (because the hemodynamic response variable is produced by a
>> generalized convolution of neuronal treatment effects). (ii) Even if
>> is this were possible, the power analysis would have to be replicated
>> about one hundred thousand times to cover the different standard
>> errors of the treatment effect estimators at each voxel (volume
>> element). (ii) Even if this were done, the results would not be useful
>> because of the multiple comparison problem, which would be more severe
>> for some contrasts relative to others (depending on the differential
>> search volumes for each contrast). In short, it is naive to apply
>> power analyzes developed for inference on discrete data to topological
>> inference with SPM. The most useful approach, which is now standard in
>> the field, is to use previous similar studies with n-subjects that
>> have been able to reject the null hypothesis in one or more voxels
>> (adjusted to control family wise error). This establishes a lower
>> bound on the number of subjects required
I am about to submit an EU application for a project that looks to scan children with conduct problems and typically developing children and follow a subset of these kids longitudinally (both with another scan + beh assessment). I am basing my numbers to be generously larger than previous single time point or longitudinal assessments of conduct problems and other childhood disorders using fMRI. I could probably come up with some half baked power calculation too, but I am never convinced with these in the context of fMRI studies, particularly when trying to pitch for new paradigms. But I am also not capable of putting this viewpoint particularly eloquently.
What would be your recommended approach here and would you be happy to endorse the above or provide something else as a personal communication - or perhaps point me to a relevant paper or web resource (I have done a quick check and was not able to pinpoint anything straightforward, i.e. I could quote something like Desmond & Glover, 2002 but it seems to me that it would be approaching useless to plead my case using this reference as I am looking at kids, with different paradigms + some of the kids are not typical)?
Extremely sorry to bother you with this.