Three statistical problems related to criterion-referenced testing are investigated: estimation of the likelihood of a false-positive or false-negative decision with a mastery test, estimation of true scores in the Compound Binomial Error Model, and comparison of the examinees to a control. Two methods for estimating the likelihood of false-positive and false-negative errors were developed and compared. For both procedures, it was found that when observations are generated according to a two-term approximation to the compound binomial, there was negligible effect on the accuracy of the estimates. Neither of the two estimation procedures consistently gave more accurate results. The estimation of true scores in the compound binomial error model was also explored. Findings showed that it was often possible to obtain a nontrivial improvement over the sample when simultaneously estimating the true score of several examinees; these estimation techniques appeared to be robust in terms of departure from the binomial distribution. The final investigation dealt with the standards used when making a mastery/nonmastery decision in terms of a particular skill. It was suggested that the true scores of the examinees be compared to a control population when defining minimum competency. (Author/MV)