This final report of a National Institute of Education project explores Bayesian statistical analysis as a paradigm for educational impact studies, particularly studies on the education of the disadvantaged. The position of the report is that much of what is wrong with educational research can be attributed to the use of an inappropriate model for making inferences. The author presents and discusses advantages of Bayesian inference over the "sampling-theory" framework of inference. Particular attention is paid to the demonstration of advantages of the Bayesian paradigm as a basis for representing knowledge when the data are "weak." Computer programs are provided to facilitate the application of Bayesian analysis to the sort of data most frequently encountered in educational evaluation. Also emphasized is the need for careful and explicit specification of the data-generating model before undertaking data analysis. (Author/JKS)