The Simpson's paradox and fMRI: Similarities and differences between functional connectivity measures derived from within-subject and across-subject correlations.

Task-related functional connectivity (fc-MRI) indexes the interaction of brain regions during cognitive tasks. Two general classes of methods exist to investigate fc-MRI: the most widely-used method calculates temporal correlations between voxels/regions within subjects, and then determines if within-subject correlations are reliable across subjects (ws-fcMRI); the other calculates the average (BOLD) signal within voxels/regions and then performs correlations across subjects (as-fcMRI). That is, while both methods rely on correlational techniques, the level at which correlations are calculated is fundamentally different. While conceptually distinct, it is not known how well these two methods of fc-MRI analyses converge on the same findings. The current study addresses this question across a number of analyses. First, using default-mode network regions as seeds, we show that as-fcMRI does not strongly predict ws-fcMRI during episodic simulation tasks. Next, we show that the relationship between as-fcMRI and ws-fcMRI is contingent on whether correlations are calculated between regions from the same functional network (default mode or dorsal attention networks) or between regions from different functional networks. Lastly, we compare seed partial least squares (PLS) - a well-established as-fcMRI method - with a novel version of seed PLS that combines the multivariate approach of PLS analyses and within-subject correlations. The results showed that while many regions exhibited congruent as-fcMRI and ws-fcMRI effects, in some regions the two analyses produced effects in opposite directions. Results are discussed in relation to the Simpson's Paradox, a phenomenon in which across-subject correlations are reversed within individuals present in a sample. Overall, our results suggest that the findings of as-fcMRI do not always map onto those from ws-fcMRI. We end by discussing the advantages associated with using ws-fcMRI to assess the task-related interactions between brain regions.