Steve,
> Can someone give me definitions for the corrected and uncorrected p-values
> at the cluster level, appearing in spm99 output? I read the Friston et al
> 1994 HBM paper and looked at spm_list.m and spm_P.m, but it's still not
> clear to me what these 2 p values constitute.
I'll take a stab at this, but I wonder what others think.
Set up
V voxels
W Smoothness (W = [w1 w2 w3])
u Threshold
k cluster size
p_uc uncorrected p-value
p_c corrected p-value
Take I. Statistically Anal Description
Let's say I randomly generate statistic images, over and over
again; each image has V voxels and smoothness W. They are "null"
images, in that they have no signal, the null hypothesis is true
everywhere. I threshold each at u.
In the long-run, on average, the proportion of random images that have
a cluster of size k *or* *larger* is p_c. The am looking for clusters
anywhere in the brain; this is what makes these p-values corrected
p-values.
The uncorrected p-values remove the search over the whole brain. I
assume it goes something like this: For each random image, uniquely
identify a single cluster (e.g. the cluster nearest to point (x,y,z));
if no cluster matches the critieron *throw* *out* that random image
(e.g. if there are no clusters at all).
Then, in the long-run, on average, the proportion of random images
whose uniquely identified cluster is of size k or larger is p_uc.
There is no search over the brain, and hence these are not corrected
p-values.
Take II. Informal Description
The corrected p-value p_c measures how likely a cluster of size k is
(under the null hypothesis of no signal), accounting for a search
over the whole brain.
The uncorrected p-value p_uc does the same but does not account for the
search over the brain; it assumes that you have uniquely identified
this cluster somehow
What do people think?
-Tom
-- Thomas Nichols -------------------- Department of Biostatistics
http://www.sph.umich.edu/~nichols University of Michigan
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-------------------------------------- Ann Arbor, MI 48109-2029
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