```Israr,

Let me start of on the issue of means, sd, r, and t-statistics (basic ideas).
(1) beta ~ weight of a particular IV (e.g. column)
(2) sd ~ weight of overall variance based on covariance of betas
(3) beta=sd(XY)/var(X); r=beta*sd(x)/sd(y) {for linear regression, for
multiple linear regression and general linear models, you compute
partial correlations}
(4) r=sqrt(t^2/(t^2+df) OR t=beta-0/sd

The beta and residual of the model form the basis of the r, not the
other way around. Everything is test against a mean of 0. Since fMRI
values are non-zero, a constant is included to account for the
non-zero mean of the data. It is the betas (not r) that are compared
statistically.

Contrasts:
Run1-C1 Run1-C2 Run2-C1 Run2-C2 Run3-C1 Run3-C2 Run4-C1 Run4-C2
1 -1 1 -1 0 0 0 0 tests C1>C2 for pretreatment
0 0 0 0 1 -1 1 -1 tests C1>C2 for postreatment
1 -1 1 -1 -1 1 -1 1 tests  (C1>C2 for pretreatment) > (C1>C2 for postreatment)

1 means you add the beta, -1 means you subtract the beta, AND it is
the sum of the added and subtracted betas that give you the value to
compare against 0.

T-statistic (matrix notation not included):
T=Contrast*beta/(ResMS*Contrasts*covbeta*Contrasts)
which can be thought of as effect-mean (effect-0) divided by the variance.

Now, if you have multiple subjects, you take the Contrast*beta part of
the T-statistic(con_* images) to the second level modelling.

Let me know if that clarified the issue.

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
Office: (773) 406-2464
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