Four different procedures were used for estimating the proportion of persons who would be classified consistently as either passing both of two parallel tests or failing both. These four methods were applied at each of four different mastery level scores for each of three different length tests. Data were based on 50 replications of each procedure for samples of 30 cases and 300 cases randomly drawn from a population of l586 cases. The outcomes of these sampling experiments were compared with the parameter values for the population. In addition to this study, four other papers on related topics are attached. "Empirical Investigation of Procedures for Estimating Reliability for Mastery Tests" discusses the data presented in the previous paper. The next paper, "Estimating the Probability of Correct Classification in Mastery Testing," discusses the Keats-Lord model used in the preceding papers. "Further Comments on Reliability for Mastery Tests" explores the use of coefficients of classification consistency. The last paper, "Confirmatory Inference and Geometric Models," discusses the relationship between exploratory and confirmatory approaches to collecting and analyzing data and the application of geometric models to these approaches. (CTM)