This chapter examines the core analytic elements of randomized experiments for social research. Its goal is to provide a compact discussion for faculty members, graduate students, and applied researchers of the design and analysis of randomized experiments for measuring the impacts of social or educational interventions. Design issues considered include choosing the size of a study sample and its allocation to experimental groups, using covariates or blocking to improve the precision of impact estimates, and randomizing intact groups instead of individuals. Analysis issues considered include estimating impacts when not all sample members comply with their assigned treatment and estimating impacts when groups are randomized. (Contains 2 tables, 2 figures, and 32 footnotes.) [This working paper will be published as a chapter in the forthcoming "Handbook of Social Research" by Sage Publications, Inc. It was supported by the Judith Gueron Fund for Methodological Innovation in Social Policy Research at MDRC, which was created through gifts from the Annie E. Casey, Rockefeller, Jerry Lee, Spencer, William T. Grant, and Grable Foundations.]