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.
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