The classical estimate of a binomial probability function is to estimate its mean in the usual manner and to substitute the results in the appropriate expression. Two alternative estimation procedures are described and examined. Emphasis is given to the single administration estimate of the mastery test reliability. (Author/CTM)

A procedure is described for determining the minimal length of a mastery test given certain constraints. The procedure assumes that the testor is indifferent to misclassifying some testees who score within a specified range about the passing score. An example and table are provided. (JKS)

Several Bayesian approaches to the simultaneous estimation of the means of k binomial populations are discussed. This has particular applicability to criterion-referenced or mastery testing. (Author/JKS)

Wilcox (1977) examines two methods of estimating the probability of a false-positive on false-negative decision with a mastery test. Both procedures make assumptions about the form of the true score distribution which might not give good results in all situations. In this paper, upper and lower bounds on the two possible error types are described…

Emrick's proposed method for determining a mastery level cut-off score is questioned. Emrick's method is shown to be useful only in limited situations. (JKS)

The problem of determining an optimal passing score for a mastery test is discussed, when the purpose of the test is to predict success on an external criterion. For the case of constant losses for the two possible error types, a method for determining passing scores is derived. (Author/JKS)

A mastery test is frequently described as follows: an examinee responds to n dichotomously scored test items. Depending upon the examinee's observed (number correct) score, a mastery decision is made and the examinee is advanced to the next level of instruction. Otherwise, a nonmastery decision is made and the examinee is given remedial work. This…

False-positive and false-negative decisions are the two possible errors committed with a mastery test; yet the estimation of the likelihood of committing these errors has not been investigated. Two methods of this type of estimation are presented and discussed. (Author/JKS)

This paper discusses how certain recent technical advances might be extended to examine proficiency tests which are conceptualized as representing a variety of skills with one or more items per skill. In contrast to previous analyses, errors in the item level are included. (Author/BW)

A problem of considerable importance in certain educational settings is determining how many items to include on a mastery test. Applying ranking and selection procedures, a solution is given which includes as a special case all existing single-stage, non-Bayesian solutions based on a strong true-score model. (Author/JKS)

Methods are described for obtaining upper and lower bounds to both false-positive and false-negative decisions with a mastery test. These methods make no assumptions about the form of the true score distribution. (CTM)

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…

Mastery tests are analyzed in terms of the number of skills to be mastered and the number of items per skill, in order that correct decisions of mastery or nonmastery will be made to a desired degree of probability. It is assumed that a random sample of skills will be selected for measurement, that each skill will be measured by the same number of…