7.9. False Discovery Rate (FDR)

These are notes by B. Douglas Ward, written in the Good Ol’ Days.

7.9.1. Program 3dFDR

Purpose

Program 3dFDR implements the False Discovery Rate (FDR) algorithm for thresholding of voxelwise statistics. Instead of controlling for alpha (the probabilty of a false positive anywhere in the volume), the FDR algorithm controls for the proportion of false positives relative to the number of detections.

Program input consists of a dataset containing one (or more) statistical sub-bricks. Output consists of a bucket dataset with one sub-brick for each input sub-brick. For non-statistical input sub-bricks, the output sub-brick is a copy of the input. However, statistical input sub-bricks are replaced by the corresponding FDR values, as follows:

For each voxel, the minimum value of q is determined such that

\[E(FDR) \leq q\]

leads to rejection of the null hypothesis in that voxel. Only voxels inside the user specified mask (optional) will be considered. These q-values are them mapped to z-scores for compatability with the AFNI statistical threshold display, i.e.,

\[{\rm input~stat} \rightarrow p \mbox{-value} \rightarrow {\rm FDR}~q \mbox{-value} \rightarrow {\rm FDR}~z \mbox{-score}\]

These calculations are performed independently for each statistical sub-brick.

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7.9.2. ... Full Enlightenment

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