SPM/Power Analysis

See this thread on the SPM mailing list:

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). (i) 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