A Bayesian solution is suggested to the problem of jointly estimating "k is greater than 1" binomial parameters in conjunction with the problem of testing, in a Bayesian sense, the hypothesis "H" of parametric homogeneity. Applications of the estimates are illustrated with several types of data, including ophthalmological…

The effect of person misfit to an item response theory model on a mastery/nonmastery decision was investigated. Furthermore, it was investigated whether the classification precision can be improved by identifying misfitting respondents using person-fit statistics. A simulation study was conducted to investigate the probability of a correct…

I. Klugkist, O. Laudy, and H. Hoijtink (2005) presented a Bayesian approach to analysis of variance models with inequality constraints. Constraints may play 2 distinct roles in data analysis. They may represent prior information that allows more precise inferences regarding parameter values, or they may describe a theory to be judged against the…

Recent developments in cognitive psychology suggest models for knowledge and learning that often fall outside the realm of standard test theory. This paper concerns probability-based inference in terms of such models. The essential idea is to define a space of "student models"--simplified characterizations of students' knowledge, skill,…

Bayesian network models offer a large degree of flexibility for modeling dependence among observables (item outcome variables) from the same task that may be dependent. This paper explores four design patterns for modeling locally dependent observations from the same task: (1) No context--Ignore dependence among observables; (2) Compensatory…

Three separate papers are included in this report. The first describes a two-stage procedure for choosing from among several instructional programs the one which maximizes the probability of passing the test. The second gives the exact sample sizes required to determine whether a squared multiple correlation coefficient is above or below a known…

The development of an index reflecting the probability that the observed correspondence between multiple choice test responses of two examinees was due to chance in the absence of copying was previously reported. The present paper reports the implementation of a statistic requiring less restrictive underlying assumptions but more computation time…

Statistical methods are presented for studying "correlates of diversity," defined as characteristics of educational organizations that predict dispersion on the dependent variable. Strategies based on exact distribution theory and asymptotic normal approximation are considered. (TJH)

Advances in cognitive research increase the need for assessment that can address the processes and the strategies by which persons solve problems. Several psychometric models have been introduced to handle claims cast in information-processing terms, explicitly modeling performance in terms of theory-based predictions of performance. Cognitively…

Two procedures for classifying examinees into categories, one based on the sequential probability ratio test (SPRT) and the other on sequential Bayes methodology, were compared to determine which required fewer items for classification. Results showed that the SPRT procedure requires fewer items to achieve the same accuracy level. (SLD)

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…

The asymptotic posterior normality of latent variable distributions is established under very general and appropriate hypotheses, providing a probabilistic basis for assessing ability estimation/prediction accuracy in the long test case, as well as a first step in making the Dutch Identity conjecture rigorous. (SLD)

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

Standard item response theory (IRT) models posit latent variables to account for regularities in students' performance on test items. They can accommodate learning only if the expected changes in performance are smooth, and, in an appropriate metric, uniform over items. Wilson's "Saltus" model extends the ideas of IRT to development that…

Since the primary purpose of classical testing is to rank order examinees consistently, the absolute value of the true score has been relatively unimportant. However, the major purpose of criterion referenced testing is to estimate the true capabilities of examinees to perform specific tasks. Hence, the problems of true score determination assume…