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Additional info for Clinical Functional MRI: Presurgical Functional Neuroimaging (Medical Radiology Diagnostic Imaging)
Note that a logical “and” operation is deﬁned for Boolean values (true/ false) but that t values associated with individual contrasts can assume any real value. e. the signiﬁcance level of the conjunction contrast is setl to the signiﬁcance level of the contrast with the smallest t value: tc ∧ c = min(tc , tc ) . 4 Multicollinear Design Matrices Multicollinearity exists when predictors of the design matrix are highly intercorrelated. To assess multicollinearity, pairwise correlations between predictors are not sufﬁcient.
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. Since the variance within the two conditions is smaller in (b) than in (a), the estimated effect is more likely to correspond to a true difference in (b) than in (a). 05). A statistical analysis, thus, does not prove the existence of an effect, it only suggests “to believe in an effect” if it is very unlikely that the observed effect has occurred by chance.
Goebel Fig. 17. Three GLMs ﬁtting the same data with different design matrices. Top row shows residuals, second row predicted (green) and observed (blue) voxel time course. The design matrix on the left contains only one predictor, the constant term. The estimated beta weight (b0) scales the constant term to the mean signal level. The design matrix in the middle adds a predictor for “green” main condition. The estimated beta weights (b0, b1) scale the predictors and the weighted sum explains more variance than the ﬁ rst model, but residual variance is still high.