Written by members of the Wellcome Department of Imaging Neuroscience
Worsley KJ, Friston KJ (1995)
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.
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