fMRI_4: Analysis of fMRI time-series revisited - again
Worsley KJ & Friston KJ (1995)
NeuroImage 2:173-181
Abstract
Friston et al (1995) presented a method for detecting activations
in fMRI time-series based on the general linear model and a
heuristic analysis of the effective degrees of freedom. In this
communication we present correct results that replace those of the
previous paper and solve the same problem without recourse to
heuristic arguments. Specifically we introduce a proper and
unbiased estimator for the error terms and provide a more
generally correct expression for the effective degrees of
freedom. Our previous estimates of error variance were biased,
and in some instances could lead to a 10-20% overestimate of Z
values. Although the previous results are almost correct for
random repressors , that were chosen for validation, the present
results are correct for any covariate or waveform. We comment on
some aspects of experimental design and data analysis in the light
of the theoretical framework discussed here.
This paper provides a more thorough and correct mathematical
treatment of some of the statistical equations presented in the
previous paper. It also discusses the ways in which theory can
impinges upon experimental design and the treatment of data (e.g.
spatial smoothing).