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> > 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 > > Disclaimer: This e-mail is intended for the addressee(s) only, and may > also be confidential. Any review, retransmission, or other use of this > information by persons other than the addressee is strictly prohibited. > If you are not the addressee or received this by mistake, please contact > the sender and delete the material from all your computers. > > ------------------------------------------------------------------------ > -- William D. Penny Wellcome Department of Imaging Neuroscience University College London 12 Queen Square London WC1N 3BG Tel: 020 7833 7475 FAX: 020 7813 1420 Email: [log in to unmask] URL: http://www.fil.ion.ucl.ac.uk/~wpenny/