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Extra resources for Clinical Functional MRI: Presurgical Functional Neuroimaging (Medical Radiology Diagnostic Imaging)
Fortunately the beta values estimated by the GLM are correct estimates (unbiased) even in the presence of serial correlations. e. t or F values are higher than they should be. It is, thus, recommended to correct for serial correlations, which can be performed with several approaches. In pre-whitening approaches, autocorrelation is estimated and removed from the data and the model, and the GLM is re-ﬁtted. In pre-colouring approaches, a known (strong) autocorrelation structure is imposed on the data, which is then properly handled by a more complex estimation procedure (generalized least squares).
Note that one would obtain the same mean values and, thus, the same difference in cases (a) and (b). Despite the fact that the means are identical in both cases, the difference in case (b) seems to be more “trustworthy” than the difference in case (a) because the measured values vary less in case (b) than in case (a). Statistical data analysis goes beyond simple subtraction by taking into account the amount of variability of the measured data points. Statistical analysis essentially asks how likely it is to obtain a certain effect if there would be only noise ﬂuctuations.
05), one rejects the null hypothesis and accepts the alternative hypothesis stating that there exists a true effect. Note that the decision to accept or reject b Fig. 14a,b. Principle of statistical data analysis. An experiment with two conditions (“Stim” and “Rest”) has been performed. a Time course obtained in area 1. b Time course obtained in area 2. Calculation and subtraction of Mean 1 (“Rest” condition) from Mean 2 (“Stim” condition) leads to the same result in (a) and (b). In a statistical analysis, the estimated effect (mean difference) is related to its uncertainty, which is estimated by the variability of the measured values within conditions.