>
> Dear Shary,
> We have just been discussing your observation that uncorrected
> p-values based on extent can be greater than the corrected
> p-values based on spatial extent. I thought it would be useful to
> share this discussion:
> The uncorrected p-value is the probability a cluster (of size n) has k
> or more voxels
> p = p(n > k)
> given that the cluster exists (i.e., p(n > 0) = 1). This can be useful
> for making inferences about a cluster you have identified as
> interesting, based on its extent. The corrected p-value is the
> probability of getting any cluster of k or more voxels in the search
> volume
> P = 1 - spm_Pcdf(0,E(S).p)
> where spm_Pcdf is the cumulative density function for the Poisson
> distribution and E(S) is the rate of maxima (i.e., expected number
> in the search volume S), approximated with the Euler characteristic
> (see
> Friston KJ, Holmes A, Poline JB, Price CJ, Frith
> CD.
> Detecting activations in PET and fMRI: levels of inference and power.
> Neuroimage. 1996 Dec;4(3 Pt 1):223-35
> for more details).
> At small values P is approximately equal to E(S).p. You can see
> that the corrected p-value P can be less that the uncorrected
> p-value if E(S) is small.
> Heuristically, if you used a low height threshold you might expect 4
> clusters on average, by chance (i.e., E(S) = 4). In this instance
> the probability of getting one or more clusters larger than k voxels
> is greater than the probability of any single cluster being greater
> than k voxels. (i.e., P > p). However, when you use a high height
> threshold E(S) is small and P < p.
>
> More specifically, for cluster-level inference, we can write
>
> P = 1 - exp (-E(S). p)
>
> Then P < p if
>
> E(S) < [- log(1-p)]/p
>
> For your first inference you have p = 0.34 which means this
> threshold is E(s) < 1.22. But the expected number of clusters
> is very small: E(S)=0.05. So we expect P < p, which is indeed the
> case.
>
> This may seem counterintuitive because the corrected p-value is
> more significant than the uncorrected p-value. This happens
> because the uncorrected p-value is conditioned on the cluster
> existing. In other words, you have to identify the cluster before
> making an inference (in the same way that you have to identify
> a specific maximum before using the uncorrected p-value based
> on height).
> The uncorrected p-value based on extent is provided for situations
> in which you know a priori which cluster you want to make an
> inference about. This can be useful in making anatomically
> constrained inferences(see
> Friston KJ. Testing for
> anatomically specified regional effects. Hum Brain Mapp.
> 1997;5(2):133-6
> ).
> I hope this helps.
> Karl
(Mr.) Shahryar (Shary) Rafi-Tari wrote:
> Dear SPM authors,
>
> This is a follow up to the e-mail I sent to Dr. Ashburner. Attached
> please find an SPM2 output (two groups/SPECT/ 1 scan per subject/ANCOVA)
> showing uncorrected cluster level p value is larger than corrected
> cluster level p-value after corrected the height threshold (FWE<0.05).
> This happens with any analysis using I do with FWE and since I am going
> to write a paper on the results and report both corrected and
> uncorrected p-values, I am trying to figure this out. I greatly
> appreciate your comments.
>
> regards,
> Shary
>
> At 10:24 AM 07/10/2005 +0100, John Ashburner wrote:
>
>> Dear Shary,
>>
>> > * Why when FWE is used to correct height threshold for multiple
>> > comparisons, the cluster level uncorrected p value is larger (for
>> > instance p<0.24) than the cluster level corrected p value (for
>> > instance p<0.02)? It is usually vice versa when FWE is not use as a
>> > result of correcting it (which is logical). Is it because FWE
>> > affects only the corrected cluster level p value?
>>
>> I have no idea about this part of SPM I'm afraid. I've forwarded your
>> query
>> on the other developers to see if they have any ideas.
>>
>> Best regards,
>> -John
>
>
>
> Shahryar Rafi-Tari, M.Sc.
> Database Consultant / Imaging Analyst
> ADNI Imaging Project Coordinator at Sunnybrook
>
> 2075 Bayview Avenue
> Sunnybrook & Women's College Health Sciences Centre
> Linda C Campbell Cognitive Neurology Research Unit
> Room B630
> Toronto, Ontario, Canada M4N 3M5
>
> E-mails: [log in to unmask]
> Tel: 416-480-6100 ext. 3281
>
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> ------------------------------------------------------------------------
>
--
William D. Penny
Wellcome Department of Imaging Neuroscience
University College London
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