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This paper describes a systematic experimental and theoretical analysis of performance variations in transistors that use aligned arrays of single-wall carbon nanotubes (SWNTs) grown on quartz substrates. Theoretical models, calibrated using measurements on statistically relevant numbers of transistors that each incorporate an individual aligned semiconducting SWNT, enable separate examination of different contributors to measured variations in transistors that incorporate arrays of SWNTs. Using these models and associated experiments, we study the scaling of the statistics of key performance attributes in transistors with different numbers of incorporated SWNTs and reveal long-range spatial nonuniformities in the distributions of SWNT diameters as the main contributor to observed performance variability.