I found the following comment in the SPM manual of Dick Veltman and Chloe
Hutton.
"Serial correlations affect only statistical inference at the first level. Correction
may therefore be omitted when one is only interested in a second-level (random
effects) analysis."
After re-reading Friston et al "To smooth or not to smooth" I understand that the
bias introduced when no autocorrelation adjustment is used is only a problem
when estimating the standard error of parameter estimates, and does not affect
parameter estimates themselves. This would therefore affect first order
statistical inferences, but not second level analyses based only on the value of
parameter estimates across subjects.
Is this correct? Is temporal smoothing or autocorrelation adjustment
uneccessary at the first level when resulting parameter estimates will only be
used for second level analysis?
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