–3–
3dDeconvolve and Ordinary Least Squares (OLSQ)
¥OLSQ = consistent estimator of FMRI time series fit parameter vector b
H No matter what the temporal (AKA serial) correlation structure of the noise
oÒConsistentÓ means that if you repeated the identical experiment infinitely many times, and averaged the estimated value (e.g., b ; variance), result would be the true value
¥But OLSQ estimate of time series noise variance is not consistent when serial correlation is present
HOLSQ variance estimator will usually be biased too small with serial correlation
¥Variance estimate is in denominators of formulas for t- and F-statistics
HResult: individual subject t- and F-values will be too large and/or their DOF parameters will be too large
HUpshot: Significance of individual subject activations will be over-estimated (p-values will be too small)
HThresholded individual subject FMRI maps might show too much activation
HObvious impacts on ROIs generated directly from individual subject activation maps (e.g., for connectivity analysis)
HHowever, statistics taking into account serial correlation can be too conservative, and understate the extent of the ÒtrueÓ regions of activation
o For this reason, and to avoid selection bias, perhaps it is best to define FMRI-derived ROIs using a spherical Òpunch outÓ around each activation map peak