The Benjamini & Hochberg (1995) False Discovery Rate (FDR) procedure finds a threshold such that the expected FDR is at most alpha (e.g. 0.05). 'vfdr' returns this critical threshold and applies that threshold to a map of z-values.
Reference:
Benjamini and Hochberg (1995). Controlling the False Discovery Rate: A
Practical and Powerful Approach to Multiple Testing. J Royal Stat Soc,
Ser B. 57:289-300.
In the fMRI context, the FDR can be found in
Reference:
Christopher R. Genovese, Nicole A. Lazar, Thomas E. Nichols (2002).
Thresholding of statistical maps in functional neuroimaging
using the false discovery rate. NeuroImage 15:870-878.
For a given threshold on a statistic image, the False Discovery Rate is the proportion of supra-threshold voxels which are false positives. Recall that the thresholding of each voxel consists of a hypothesis test, where the null hypothesis is rejected if the statistic is larger than the threshold. In this terminology, the FDR is the proportion of rejected tests where the null hypothesis is actually true.
A FDR procedure produces a threshold that controls the expected FDR at or below alpha (implemented in 'vfdr'). The FDR-adjusted p-value for a voxel is the smallest alpha for which the voxel is supra-threshold.
The Benjamini and Hochberg procedure is the following:
The False Discovery critical height threshold can be computed for zmaps.
vfdr -in zmap.v
this call yields the following output:
> vfdr -in zmap.v -out map.v significant: 2317 of 10759 FDR threshold: p= 0.01085, z= 2.29554 p0= 0.010851 areas with less than 3 voxels deleted. significant voxels: 2316 vfdr: done.
Note that p is set to 1 for all voxels with negative z-values. If negative z-scores are to be analyzed, 'vfdr' can be called with the option '-sign neg' in the following way:
vfdr -in zmap.v -sign neg
The z threshold can be applied to the input z-map using vfdr with the option '-out'. Overmore, a minimum area size in mm^3 can be specified:
vfdr -in zmap.v -minsize 81 -out map.v