Using data from the Westinghouse Learning Corporation Study, the effect of the Head Start Program on cognitive achievement in preschool children is examined. The use of statistical models to evaluate programs which non randomly assign children to "treatment" and "control" groups is discussed. Necessary conditions for unbiased estimation of program effects are demonstrated. A refined set of empirical estimates of Head Start effects is presented using multiple regression techniques. The results of this examination generally support the pessimistic findings of the Westinghouse study. It was indicated that recent Head Start programs have only a short term impact on minority group children and on white children from mother-headed families. Some qualifications to these findings, however, are expressed. These fall chiefly into the category of methodological problems presented by the non random nature of the population samples in studies such as this one. (Author/GC)