The false positive rates (FPR) for surface-based group analysis of cortical thickness, surface area, and volume were evaluated for parametric and non-parametric clusterwise correction for multiple comparisons for a range of smoothing levels and cluster-forming thresholds (CFT) using real data under group assignments that should not yield significant results. For whole cortical surface analysis, thickness showed modest inflation in parametric FPRs above the nominal level (10% versus 5%). Surface area and volume FPRs were much higher (20–30%). In the analysis of interhemispheric thickness asymmetries, FPRs were well controlled by parametric correction, but FPRs for surface area and volume asymmetries were still inflated. In all cases, non-parametric permutation adequately controlled the FPRs. It was found that inflated parametric FPRs were caused by violations in the parametric assumptions, namely a heavier-than-Gaussian spatial correlation. The non-Gaussian spatial correlation originates from anatomical features unique to individuals (e.g., a patch of cortex slightly thicker or thinner than average) and is not a by-product of scanning or processing. Thickness performed better than surface area and volume because thickness does not require a Jacobian correction.