> For the GLT matrix suggestion by Kyle (first seven rows),
> extracting t statistics for each row (each contrast), thresholding the
> SPM and then taking the union would answer the question, "For this
> voxel, does Condition 1 differ from any other single condition?" I
> think this is what you are suggesting above, as a conjunction analysis.

Yes, you are right.

> Whereas testing the F statistic for that GLT would answer the
> question, "For this voxel, does any condition differ from any other
> condition?" As such, the F stat will for the first-7 rows of kyles GLT
> can be significant if even A does not significantly differ from anything

For question "For this voxel, does any condition differ from any other
condition?" we would need his original GLT matrix of 28X8. However the problem of rank deficiency doesn't allow such an F test, and GLT with the first 7 rows would only catch the differences between the 1st condition and the rest, as you have demonstrated.

> When calculating the F statistic for the GLT, do the regressors
> have to be orthogonal?

No, they don't have to, but my understanding is that the GLT matrix has to satisfy rank(GLT) < # of Rows.

> If we wanted to ask, "For this voxel, does any condition differ
> from any other condition?" would it be best to use the following
> GLT matrix?:
>
> 1 1 1 1 0 0 0 0
> 1 1 -1 -1 0 0 0 0
> 1 -1 0 0 0 0 0 0
> 0 0 1 -1 0 0 0 0
> 0 0 0 0 1 1 -1 -1
> 0 0 0 0 1 -1 0 0
> 0 0 0 0 0 0 1 -1
>
> instead of the first 7 lines of Kyle's GLT matrix?

I don't see the reasoning yet: Can you elaborate this a little more why the original matrix 28X8 can be reduced to the above matrix of 7X8?

Gang