The Rule Space Model, a cognitive error diagnostic methodology, is discussed, and the philosophy behind it is related to the question of what really determines item response curves. The Rule Space approach integrates Item Response Theory and the algebraic theory of databases. An application of Graph Theory is introduced as a way to acquire a list…

The classification problem in educational testing is a decision problem. One must assign subjects to one of several available treatments on the basis of test scores, where the success of each treatment is measured by a different criterion. Examples of classification decisions include individualized instruction, counseling, and clinical settings.…

The applicability is explored of the Bayesian random-effect analysis of variance (ANOVA) model developed by G. C. Tiao and W. Y. Tan (1966) and a method suggested by H. K. Suen and P. S. Lee (1987) for the generalizability analysis of autocorrelated data. According to Tiao and Tan, if time series data could be described as a first-order…

This final report of a National Institute of Education project explores Bayesian statistical analysis as a paradigm for educational impact studies, particularly studies on the education of the disadvantaged. The position of the report is that much of what is wrong with educational research can be attributed to the use of an inappropriate model for…

In the methods and approaches developed for estimating the operating characteristics of the discrete item responses, the maximum likelihood estimate of the examinee based upon the "Old Test" has an important role. When Old Test does not provide a sufficient amount of test information for the upper and lower part of the ability interval,…

The use of subjective probability as a theoretical model for enrollment forecasting is proposed, and the results of an application of subjective probability to enrollment forecasting at the University of Toledo are reported. Subjective probability can be used as an enrollment forecasting technique for both headcount and full-time equivalent using…

A system of computer-assisted data analysis (CADA) was developed at the University of Iowa to handle the mechanical, arithmetical and computational tasks associated with Bayesian statistical analysis. The original programs were subsequently expanded and a CADA monitor constructed to aid their use; a search was then undertaken to find a means of…

An experimental study of the efficiency of human information processing is based on the Bayesian model for simple hypothesis testing with fixed binomial sampling. Each of 60 subjects is analyzed with separate ANOVAs focusing on two efficiency variables. Sample size and critical value are also analyzed. Subjects show very different utilization of…

The Libby-Novick class of three-parameter generalized beta distributions is shown to provide a rich class of prior distributions for the binomial model that removes some restrictions of the standard beta class. A numerical example indicates the desirability of using these wider classes of densities for binomial models. (Author/BW)

A universal criterion scale is applied to the direct estimation of validity for various groups of law school applicants and to the testing of the assumptions underlying the more familiar extrapolation methods. Data from American law schools are used to illustrate the procedures. (Author/BW)

The Bayesian inferential process is modified for use in an aggregate meta-analytic evaluation. Compared with the average effect size meta-analytic approach, the Bayesian approach was more sensitive, more consistent and more powerful. This approach is recommended when primary data are not available and when all evaluations involve comparisons of…

Context for the application and specialization of a Bayesian linear model is m-group regression and the application to the prediction of grade point average. Specialization involves the assumption of homogeneity of regression coefficients (but not intercepts) across groups. Model's predictive efficiency is compared with that of the full m-group…

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…