Their suggestion:
T-stat cluster statistic
The spatial (brain-space) covariance of the image based on the regularized Guass-Markov equation would be
CovBeta = inv(X'*X+lambda*I) * R
Where R is the channel-channel covariance and X is the forward model.
If your ROI/cluster is given by the contrast vector c = [0 0 0 1 1 1 1…] where the length of c is the number of voxels and is 1 in the cluster and 0 else, then the T-test is
T = c * Beta / sqrt(c* CovBeta * c')
This would be the T-test over the cluster accounting for the fact that neighboring voxels in the reconstruction are not independent.
The F-test version would be something more like
VarianceExplained by cluster = sum ( X * c * Beta )^2 /(k-1)
Variance of residual = sum ( Y - X*c*beta) ^2 ) / (n-k)
F = SSM/SSR
I think n in this case the number of channels and k is 2 (?) [the number of clusters + the DC term) . But, check this.
I don't know how to implement this in my data. I'm still reading/learning about the options in 3dclustsim, so there may be a way to address these things. Any advice is appreciated!
