table of contents
LIPSIA     False Discovery Rate
vfdr
The program 'vfdr' provides one approach to the correction of results from statistical significance tests for multiple comparisons.
Background

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.

FDR procedure

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:


Computing the critical height threshold

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

Parameters of 'vfdr':
-help
Prints usage information.
-in
Input file. Default: (none)
-out
Thresholded output file. Default: (none)
-sign [ pos | neg ]
Whether pto analyze ositive or negative values.
Default: pos
-alpha
Threshold. Default: 0.05
-minsize
Minimum area size in mm^3. Default: 81


Max Planck Institute for Human Cognitive and Brain Sciences. Further Information: lipsia@cbs.mpg.de
Copyright © 2007 Max Planck Institute for Human Cognitive and Brain Sciences. All rights reserved.