A new direct and short proof is offered for the monotone likelihood ratio for the sum of independent Bernoulli random variables through use of an inequality by Marcus and Lopes (1957) on elementary symmetric functions. (SLD)

Two indices for assessing the efficiency of decisions in mastery testing are proposed. The indices are generalizations of the raw agreement index and the kappa index. Empirical examples of these indices are given. (Author/JKS)

Simulated data based on five test score distributions indicate that a slight modification of the asymptotic normal theory for the estimation of the p and kappa indices in mastery testing will provide results which are in close agreement with those based on small samples from the beta-binomial distribution. (Author/BW)

The use of Cohen's kappa index as a measure of the reliability of multiple classifications is developed. Special cases of the index as well as the effects of test length on the index are also explored. (JKS)

A model for the setting of mastery cut scores is presented. The model, based on the beta-binomial test distribution, allows for hand calculation of cut scores. The model provides a simple way to explore the consequences of selecting a particular cut score. (Author/JKS)

In mastery testing, the raw agreement index and the kappa index may be estimated via one test administration when the test scores follow beta-binomial distributions. This paper reports formulae, tables, and a computer program which facilitate the computation of the standard errors of the estimates. (Author/CTM)

A procedure for estimating the rates of false positive and false negative classification in a mastery testing situation is described. Formulas and tables are described for the computations of the standard errors. (Author/JKS)

A general model along with four illustrations is presented for the consideration of budgetary constraints in the setting of passing scores in instructional programs involving remedial action for poor test performers. Budgetary constraints normally put an upper limit on any choice of passing score. Given relevant information, this limit may be…

A Bayesian framework for making mastery/nonmastery decisions based on multivariate test data is described. Overall, mastery is granted if the posterion expected loss associated with such action is smaller than the one incurred by denying mastery. (Author/JKS)

A nonrandomized minimax solution is presented for passing scores on mastery tests using the binomial error model. The computation does not require prior knowledge regarding an individual examinee or group test data for a population of examinees. A scheme which allows for correction for guessing is also described. (Author/JKS)

A general framework for making mastery/nonmastery decisions based on multivariate test data is described in this study. Over all, mastery is granted (or denied) if the posterior expected loss associated with such action is smaller than the one incurred by the denial (or grant) of mastery. An explicit form for the cutting contour which separates…

Assuming that the density p of the true ability theta in the binomial test score model is continuous in the closed interval (0, 1), a Bernstein polynomial can be used to uniformly approximate p. Then via quadratic programming techniques, least-square estimates may be obtained for the coefficients defining the polynomial. The approximation, in turn…

Single administration (beta-binomial) estimates for the raw agreement index p and the corrected-for-chance kappa index in mastery testing are compared with those based on two test administrations in terms of estimation bias and sampling variability. Bias is about 2.5 percent for p and 10 percent for kappa. (Author/RL)

A procedure is described for the determination of individual mastery scores when instructional units are sequenced in a linear hierarchy. It can be used when data for the entire sequence have been obtained. The process entails working backwards, from the final test to the first. (Author/JKS)

The Bayesian approach to setting passing scores, as proposed by Swaminathan, Hambleton, and Algina, is compared with the empirical Bayes approach to the same problem that is derived from Huynh's decision-theoretic framework. Comparisons are based on simulated data which follow an approximate beta-binomial distribution and on real test results from…