BOLD Statistical Analysis

The statistical analysis is performed using a T-test, performed in a voxel wise manner. The output of this test, generates statistical maps which can be displayed as an overlay on an image volume. The formula applied is

which depends on the user supplied contrasts c, the -values and the error term from the GLM estimation, as well as the design matrix X and the degrees of freedom .

Degrees of Freedom - The Effect of Temporal Smoothing

Temporal smoothing can be performed prior to estimating GLM and will affect the degrees of freedom in the T-test.

No Temporal Smoothing

If no temporal smoothing has been performed, the degrees of freedom in the estimation is equal to

where N is the number of elements in the design matrix X and rank(X) is equal to the rank of the design matrix.

Temporal Smoothing

If temporal smoothing has been performed to the design matrix and the input data prior to estimating GLM, a different formula for estimating the degrees of freedom must be applied. Here the effective degrees of freedom from the article Analysis of fMRI Time-Series Revisited - Again by Friston et.al. (1997). is applied.