Post-hoc power estimation for topological inference in fMRI.

When analyzing functional MRI data, several thresholding procedures are available to account for the huge number of volume units or features that are tested simultaneously. The main focus of these methods is to prevent an inflation of false positives. However, this comes with a serious decrease in power and leads to a problematic imbalance between type I and type II errors. In this paper, we show how estimating the number of activated peaks or clusters enables one to estimate post-hoc how powerful the selection procedure performs. This procedure can be used in real studies as a diagnostics tool, and raises awareness on how much activation is potentially missed. The method is evaluated and illustrated using simulations and a real data example. Our real data example illustrates the lack of power in current fMRI research.