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Geographic health disparities in the US reflect both compositional characteristics of residents and contextual effects of places, yet existing research rarely decomposes these mechanisms across all three nested administrative levels (tracts, counties, states) simultaneously. I apply within-between centering to eleven tract-level health outcomes, decomposing sociodemographic predictors into tract compositional sorting, between-county effects net of state differences, and between-state effects. The findings reveal, first, while tract composition explains substantial variance, between-county and between-state effects consistently exceed tract composition effects, demonstrating genuine contextual mechanisms beyond residential sorting. Second, the magnitude of contextual effects varies substantially by health outcome, with some outcomes show predominantly state-level contextual influences, whereas others primarily reflect tract-level compositional sorting. A placebo test using randomized administrative boundaries validates that observed contextual effects reflect real jurisdictional boundaries rather than statistical artifacts of the Modifiable Areal Unit Problem. Rather than debating whether composition or context matters, this decomposition framework reconciles both perspectives by identifying which geographic levels and mechanisms operate for which outcomes, providing guidance for scale-appropriate intervention strategies.