Dear all
I am interested in the GRF and statisitcs in the spm.
I carried out some simulations to understand thresholding processes in spm
and had questions about spatial extent test.
I generated the 128*128 ramdom image having the unit variance and
smoothed with a Gaussian kernel FWHM of 8 by 8.
(Matthew's program was reffer to this analysis.)
>From the spm course note, ch4, pp7,
the uncorrected p for the spatial extent test is given by equation (6)
and corrected p is given by equation (7).
And I plot the theoretical probability of the spatial extent test
when simulated images is thresholded at different Z values and different areas n.
This script is:
%-----------------------------------
%This script uses matlab functions in spm 96.
%
%The parameters of simulated images:dimension=[128 128],smoothness=[8 8],volume=128*128.
%
%The corrected p value for spatial extent test
for u=1:500;for k=1:100;pnumax(u,k)= spm_P(1,[8 8],u*0.01,k,128*128);end;end
%The uncorrected p value for spatial extent test
for u=1:500;for k=1:100;pnu(u,k)= 1-spm_kcdf(k,u*0.01,[8 8]);end;end
figure;
imagesc(pnu');
title('uncorrected p');xlabel('Z threshold * 100');ylabel('Extent threshold');colorbar
figure;imagesc(pnumax');
title('corrected p');xlabel('Z threshold * 100');ylabel('Extent threshold');colorbar
k=100;%Extent threshold
figure;plot([1:500],pnu(:,k),[1:500],pnumax(:,k));
title(['Extent threshold' int2str(k)]);xlabel('Z threshold * 100');ylabel('Probability')
u=400;%high threshold
figure;plot([1:100],pnu(u,:),[1:100],pnumax(u,:));
title(['Z threshold' int2str(u)]);xlabel('Extent threshold');ylabel('Probability')
%------------------------------------------------------------
>From the graph,the uncorrected p-value is greater than the corrected p-value
by the combination of a certain u and k.
Why is this?
In this simulation, the probability of getting one or more clusters
of size k or more, above high threshold u, almost corresponds to
the corrected p-value.
Thank you for your help,
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Takanori Kochiyama
Graduate School of Human and Environmental Studies,
Kyoto University
京都大学大学院人間・環境学研究科(総合人間学部松村研究室)
河内山 隆紀
E-mail:[log in to unmask]
Tel:+81 75 753 7862
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