# 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.

*… [end of excerpt; see below for the full document]*