Brett (and any statistician who would like to add their thoughts):

I wonder if you could comment about the use of uncorrected thresholds in 
combination with extent thresholds.

My lab routinely screens (and often publishes) results using an uncorrected 
intensity ("voxel-wise") threshold of p<0.001 in combination with an extent 
threshold of 10 voxels (applied to images re-sliced at 3x3x3 mm voxels and 
smoothed with either a 7 mm or 10 mm Gaussian kernel).  We find that this 
pretty well eliminates activation outside of any area that we could expect 
to find activation on theoretical grounds.  Another lab on campus has run 
monte carlo simulations on various intensity / extent combinations (using 
AFNI), and found a false discovery rate < 0.05 whenever the uncorrected 
Z-statistic is greater than about 4.00 -- which almost exactly corresponds 
to the Z-statistic values we find with our standard intensity/extent threshold.

If uncorrected p < 0.001 is valid when applied to a single voxel (without 
examining other brain voxels), the chance of reaching this threshold for 10 
contiguous voxels (before correcting for multiple comparisons) should be 
roughly (0.001)^10 -- which would survive the FWE correction.  This is not 
really statistically accurate, though, in part because the "activation" of 
contiguous voxels is influenced by the smoothing process.  Even after 
accounting for smoothing effects, though, the chance of 10 contiguous 
voxels reaching some statistical threshold is clearly far less than the 
likelihood of a single voxel reaching that threshold.

Since SPM does not include a toolbox for monte carlo simulations that can 
examine the likelihood of various intensity / extent combinations, I wonder 
whether there is any statistical argument which can be used to justify a 
combined intensity/extent threshold -- particularly one that would satisfy 
reviewers.

Doug Burman

At 02:26 PM 2/24/2007 +0000, Matthew Brett wrote:
>Hi,
>
>I've summarized the arguments here:
>
>http://imaging.mrc-cbu.cam.ac.uk/imaging/UncorrectedThreshold
>
>Best,
>
>Matthew

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