This case study is directed at the methods used to examine group differences when random group assignment is not a feasible option. The authors discuss how to employ propensity score matching techniques and practical issues that arise when employing such techniques. The context of using propensity score matching is embedded in a research study directed at examining the mathematics achievement of children identified as having attention deficit hyperactive disorder who received special education services compared to those who are not, using data from the Early Childhood Longitudinal Study--Kindergarten study, a large-scale nationally representative data set. Researchers matched and equated these two groups and compared them on mathematics achievement. The advantages and limitations of using propensity score matching are discussed. [This content is provided in the format of an e-book.]