¥Design analysis
_XÕX invertible but cond(XÕX) is huge ˆ linear system is sensitive ˆ difficult to obtain accurate estimates
of regressor weights
_Condition number: a
measure of system's sensitivity to numerical computation
"cond(M) = ratio of
maximum to minimum eigenvalues of matrix M
"note, 3dDeconvolve can generate both X and (XÕX)-1, but not cond()
_Covariance matrix
estimate of regressor coefficients vector b:
"s2(b) = (XÕX)-1MSE
"t test for a
contrast cÕb (including regressor coefficient):
Øt = cÕb /sqrt(cÕ (XÕX)-1c MSE)
Øcontrast for condition A only: c = [0 0 1 0
0]
Øcontrast between conditions A and B: c = [0 0 1 -1 0]
Øsqrt(cÕ (XÕX)-1c) in the denominator of the t test
indicates the relative stability and statistical
power of the experiment design
"sqrt(cÕ (XÕX)-1c) = normalized standard
deviation of a contrast cÕb (including regressor weight) ˆ these values are output by 3dDeconvolve
"smaller sqrt(cÕ (XÕX)-1c) ˆ stronger statistical power in t test, and less sensitivity in solving the normal equation of the general linear
system
"RSFgen helps find out a good design with relative small sqrt(cÕ (XÕX)-1c)