Fundamentals of Data Analysis Methods in Functional MRI - Advance Image Processing in Magnetic Resonance Imaging - page 481

compare F with F 0 (f F (u) is an F distribution with n 1 and n 2 degrees
of freedom.

3. Color-code the voxels where F > F 0 .

It is important to remark that if there is significant temporal autocorrelation
in the data, the degrees of freedom n 2 are to be “corrected” to take appropriately
into account the serial dependency between the adjacent samples of each voxel's
time course. Without this correction, the resulting value may be overestimated

(see Reference 18 and Reference 25 ). An alternative solution is to perform the

statistical tests on the time courses after they have been “prewhitened” (i.e., after

the autocorrelation has been removed; see Reference 28 and Reference 29 ] for

possible prewhitening methods).
Note that if X b X , there is a one-to-one correspondence between F in

Equation 15.20 and R 2 in Equation 15.15 and it is given by

=

n
n

R
1R

2

F = ⋅

2

(15.22)

−

2

1

15.3.1.2 Relative Contribution (RC) Maps

Statistical maps generated as described in the preceding text only provide infor-
mation about the effects of all the predictors in X b. The contribution of specific
predictors (or subsets of predictors) within X b to explaining the variance of the

observed time course can be highlighted in RC maps (see e.g., Reference 30 and
Reference 31 ). These maps are obtained by calculating at each voxel the index

given by

RC = ( b si - b s 2 ) / ( b si + b s 2 ) (15.23)

In Equation 15.23 b si is the sum of the estimates of the standardized regression
coefficients of all conditions in subset s i (we assume, for simplicity, that X b only
includes two subsets of conditions). For voxels with F greater than a given
threshold, RC is color-coded using a double-color scale (e.g., red-green color
scale). An RC value of 1 (green) indicates that a voxel time course is solely
explained with predictor set b 1 , whereas an RC value of -1 (red) indicates that a
voxel time course is explained solely with predictor set b 2 . An RC value of 0
indicates that a voxel time course is explained with equal contribution of both
predictor sets.

15.3.1.3 Specific Effects, Contrasts (t Maps)

In fMRI studies, researchers are often interested in testing the effects of a specific
condition or in comparing statistically the effects of two or more experimental
conditions. Within the GLM framework, this comparison is done by using contrast