Nonergodicity and Simpson's paradox in neurocognitive dynamics of cognitive control

Nonergodicity and Simpson's paradox present significant, yet underappreciated challenges in cognitive neuroscience. Leveraging brain imaging and behavioral data from over 4000 individuals and a Bayesian computational model of cognitive dynamics, we investigated brain-behavior relationships underlying cognitive control at both between-subjects and within-subjects levels. Strikingly, brain-behavior associations reversed across levels of analysis, revealing pervasive nonergodicity. Within-subjects analysis uncovered dissociated neural representations of reactive and proactive control and revealed that individuals who adaptively versus maladaptively regulated cognitive control exhibited distinct brain-behavior associations. Our findings demonstrate that between-subjects analyses can fundamentally mischaracterize within-individuals mechanisms, as group-level patterns not only disagreed with individual-level patterns but often reversed them. This work highlights the necessity of distinguishing between-subjects and within-subjects inferences in neuroscience, with implications for understanding cognitive mechanisms and designing personalized interventions.