The effect of the Head Start program on cognitive achievement is examined with two objectives in mind. First, we clarify the use of statistical models to evaluate programs that deal with nonrandom assignments to treatment and control groups, and we show the conditions for unbiased estimation of program effects. Second, we present a refined set of empirical estimates of Head Start effects, using multiple regression techniques. The data used are from the Westinghouse Learning Corporation study, and our results generally support their pessimistic findings, although some qualifications are in order. Head Start, a federally funded educational program, is designed to improve the cognitive and affective skills of preschool children from economically disadvantaged backgrounds. It began in 1965 under the Office of Economic Opportunity (OEO) and was based on three assumptions: that education is required to enable poor children to escape poverty in their adult years, that development during the preschool years is critical for educational success, and that children in poor families are deprived of the intellectual and cultural stimulation necessary for adequate preschool development. The program has been popular, despite the lack of clear evidence of success in achieving its goals. It survived the demise of OEO and is now administered by the U.S. Department of Health, Education, and Welfare. In 1976, 379,000 children were enrolled in the program [3].