Hello,
Not
long ago, I had a conversation on the SPM mailing list regarding the calculation
of standard error in the parameter estimates:
http://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=ind0701&L=SPM&P=R41163&I=-3&X=456A2C2D269543798D I’ve been re-visiting this problem, in the course of helping a colleague out in a simple ANOVA group level analysis in spm2. In the above e-mail, it was discussed that the standard deviation of the parameter estimates could be derived by taking the square root of the Bcov matrix produced in the workspace by spm_graph.m, or, alternatively, by taking the square root of the product of SPM.xX.Bcov the value of SPM.VResMS for the given voxel. If we divide the standard deviation by the square root of the number of samples to get the standard error, and then use the beta’s and the standard errors, we can calculate a t-test between the parameter estimates (again, at one voxel). What we found, however, was that these t-values were abnormally large. So, since this is a simple three group ANOVA, at a given voxel, the beta values for each group are simply equal to the mean of the contrast estimates entered into the design matrix for each group. So, we directly calculated the mean and standard deviation of each group’s contrast estimates at a given voxel, and this produced a standard error of the mean that was not equivalent to the standard error calculated as (using spm_graph’s Bcov) Sqrt(Bcov)/sqrt(N) (for each group). If Beta is equal to the mean of the contrast estimates entered into the design matrix (and it is) why are the standard errors in the betas not equal to the standard errors derived directly from the contrast estimates themselves? I suspect that my confusion stems from my lack of statistical background, but I would appreciate any help in resolving this conundrum. Thanks!
Allison Nugent
MRI Physicist
SNMAD/MIB/NIMH/NIH
Office:
(301)451-8863
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