This paper derives optimal rules for sequential mastery tests. In a sequential mastery test, the decision is to classify a subject as a master or a nonmaster or to continue sampling and administering another random item. The framework of minimax sequential decision theory (minimum information approach) is used; that is, optimal rules are obtained…

The purpose of this paper is to derive optimal rules for sequential mastery tests. In a sequential mastery test, the decision is to classify a subject as a master or a nonmaster, or to continue sampling and administering another random test item. The framework of minimax sequential decision theory (minimum information approach) is used; that is,…

Formulates optimal sequential rules for mastery testing using an approach derived from Bayesian sequential decision theory to consider both threshold and linear loss structures. Adopts the binomial probability distribution as the psychometric model. Provides an empirical example for concept-learning in medicine. (SLD)

A version of sequential mastery testing is studied in which response behavior is modeled by an item response theory (IRT) model. First, a general theoretical framework is sketched that is based on a combination of Bayesian sequential decision theory and item response theory. A discussion follows on how IRT based sequential mastery testing can be…

The purpose of this paper is to formulate optimal sequential rules for mastery tests. The framework for this approach is derived from empirical Bayesian decision theory. Both a threshold and linear loss structure are considered. The binomial probability distribution is adopted as the psychometric model involved. Conditions sufficient for…

This paper focuses on a version of sequential mastery testing (i.e., classifying students as a master/nonmaster or continuing testing and administering another item or testlet) in which response behavior is modeled by a multidimensional item response theory (IRT) model. First, a general theoretical framework is outlined that is based on a…

An approach to simultaneous optimization of assignments of subjects to treatments followed by an end-of-mastery test is presented using the framework of Bayesian decision theory. Focus is on demonstrating how rules for the simultaneous optimization of sequences of decisions can be found. The main advantages of the simultaneous approach, compared…

The purpose of this paper is to derive optimal rules for variable-length mastery tests in case three mastery classification decisions (nonmastery, partial mastery, and mastery) are distinguished. In a variable-length or adaptive mastery test, the decision is to classify a subject as a master, a partial master, a nonmaster, or continuing sampling…

A method is proposed for optimizing cutting scores for a selection-placement-mastery problem simultaneously. A simultaneous approach has two advantages over separate optimization. First, test scores used in previous decisions can be used as "prior data" in later decisions, increasing the efficiency of the decisions. Then, more realistic…

The purpose of this paper is to simultaneously optimize decision rules for combinations of elementary decisions. As a result of this approach, rules are found that make more efficient use of the data than does optimizing those decisions separately. The framework for the approach is derived from empirical Bayesian theory. To illustrate the…

As part of a project formulating optimal rules for decision making in computer assisted instructional systems in which the computer is used as a decision support tool, an approach that simultaneously optimizes classification of students into two treatments, each followed by a mastery decision, is presented using the framework of Bayesian decision…