Abstract: Matched sampling is a standard technique in the evaluation of treatments in observational studies. Matching on estimated propensity scores comprises an important class of procedures when there are numerous matching variables. Recent theoretical work (Rubin, D. B., and Thomas, N., 1992a, reprinted in this volume as Chapter 15) on affinely invariant matching methods with ellipsoidal distributions provides a general framework for evaluating the operating characteristics of such methods. Moreover, Rubin and Thomas (1992b, reprinted in this volume as Chapter 16) uses this framework to derive several analytic approximations under normality for the distribution of the first two moments of the matching variables in samples obtained by matching on estimated linear propensity scores. Here we provide a bridge between these theoretical approximations and actual practice. First, we complete and refine the nomal-based analytic approximations, thereby making it possible to apply these results to practice. Second, we perform Monte Carlo evaluations of the analytic results under normal and nonnormal ellipsoidal distributions, which confirm the accuracy of the analytic approximations, and demonstrate the predictable ways in which the approximations deviate from simulation results when normal assumptions are violated within the ellipsoidal family. Third, we apply the analytic approximations to real data with clearly nonellipsoidal distributions, and show that the thoretical expressions, although derived under artificial distributional conditions, produce useful guidance for practice. Our results delineate the wide range of settings in which matching on estimated linear propensity scores performs well, thereby providing useful information for the design of matching studies.