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The F-test is the mean-sums-of-squares of the effect divided by the
mean-sums-of-squares of the error. This could be computed at each
voxel, but it would be computationally intensive. Rather, matrix
algebra allows the computations to be done very quickly through
contrast matrices, projection matrices, and residual forming matrices.

The source I've used is:
http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2/pdfs/Ch7.pdf

Although, this is an spm source. The GLM is the same process is the
same. There are slight difference in the steps leading up to the GLM
though, which is why the two programs give slightly different values.

Best Regards, Donald McLaren
=================
D.G. McLaren, Ph.D.
Postdoctoral Research Fellow, GRECC, Bedford VA
Research Fellow, Department of Neurology, Massachusetts General Hospital and
Harvard Medical School
Website: http://www.martinos.org/~mclaren
Office: (773) 406-2464
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On Mon, Apr 16, 2012 at 5:07 PM, Daniel Ferreira <[log in to unmask]> wrote:
> Dear Donald,
>
> Thank you very much once again for your helpful explanations about the orthogonality matter.
>
> Now I fully understand that there is any problem with the non-orthogonality in the way that FSL runs an ANOVA (1 -1 0; 0 1 -1).
>
> Taken into account that we are asking for an ANOVA from a non-orthogonal pair of contrasts (1 -1 0: 0 1 -1) could you please detail briefly how FSL does in order to achieve and/or correct the orthogonal principle?
>
> thank you again in advance
>
> Daniel