This paper uses data from the Head Start Impact Study (HSIS), a nationally representative multisite randomized trial, to quantify variation in effects of Head Start during 2002-2003 on children's cognitive and socio-emotional outcomes relative to the effects of other local alternatives, including parent care. We find that (1) treatment and control group differences in child care and educational settings varied substantially across Head Start centers (program sites); (2) Head Start exhibited a compensatory pattern of program effects that reduced disparities in cognitive outcomes among program-eligible children; (3) Head Start produced a striking pattern of subgroup effects that indicates it substantially compensated dual language learners and Spanish-speaking children with low pretest scores (two highly overlapping groups) for their limited prior exposure to English; and (4) Head Start centers ranged from much more effective to much less effective than their local alternatives, including parent care. The following are appended: (1) Departures from the HSIS Analysis; (2) Further Detail About Our Outcome Measures; (3) Estimating Head Start Participation Effects (LATE); (4) Subgroup Estimates of the Effect of Head Start Assignment on Head Start Enrollment; (5) Baseline Balance Tests for Key Subgroups; (6) Cross-Site Grand Means and Standard Deviations for Head Start Effect Sizes Estimated With and Without a Pretest Covariate; (7) Using a Random-Effects Meta-Analysis to Estimate Variation in Program Effect Sizes Across Past Studies; and (8) A Constrained Empirical Bayes Method for Estimating Site-Specific Mean ITT Program Effects to Reflect the Estimated Cross-Site Variance of True Program Effects.