This report presents the statistical theory underlying the "RCT-YES" software that estimates and reports impacts for RCTs for a wide range of designs used in social policy research. The report discusses a unified, non-parametric design-based approach for impact estimation using the building blocks of the Neyman-Rubin-Holland causal inference model that underlies experimental designs. This approach differs from the more model-based impact estimation methods that are typically used in education research. The report discusses impact and variance estimation, asymptotic distributions of the estimators, hypothesis testing, the inclusion of baseline covariates to improve precision, the use of weights, subgroup analyses, baseline equivalency analyses, and estimation of the complier average causal effect parameter. A section on mathematical proofs is appended.