Item mappings are widely used in educational assessment for applications such as test administration (through test form assembly and computer assisted testing) and for criterion-referenced (CR) interpretation of test scores or scale anchoring. Item mappings are also used to construct ordered item booklets in the CTB/McGraw Hill Bookmark standard…

By noting that a Rasch or two parameter logistic (2PL) item belongs to the exponential family of random variables and that the probability density function (pdf) of the correct response (X=1) and the incorrect response (X=0) are symmetric with respect to the vertical line at the item location, it is shown that the conjugate prior for ability is…

Bayesian estimation procedures based on a hierarchical model for estimating parameters in the Rasch model are described. It is shown that the Bayesian procedures result in estimates with superior statistical characteristics. (Author/JKS)

The Bayesian approach to setting passing points on credentialing examinations in the health fields is considered in the context of the Normal model, and examples are given to demonstrate the procedure. An application to a credentialing examination, to determine a rational passing point, is presented. (Author/MH)

The relative merits of several methods, Bayesian and classical, for the estimation of student mastery are investigated. (Editor)

Results from two Monte Carlo studies in item response theory (comparisons of computer item analysis programs and Bayes estimation procedures) are analyzed with inferential methods to illustrate the procedures' strengths. It is recommended that researchers in item response theory use both descriptive and inferential methods to analyze Monte Carlo…

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)

A model for student retention and attrition is presented. Focus is on alternative models for the "dampening" in attrition rates as educational programs progress. Maximum likelihood estimates for the underlying parameters in each model and a Bayesian analysis are provided. (TJH)

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item and ability parameters through two joint and two marginal Bayesian procedures. Marginal procedures yielded smaller root mean square differences for item and ability, but results for larger sample size and test length were similar.…

Relationships between Bayesian ability estimates and the parameters of a normal population distribution are derived in the context of classical test theory. Formulas are presented for practical work with Bayesian ability estimates, and a numerical illustration is provided. (SLD)

This article compares three models that have been the foundation for approaches to the analysis of statistical significance in early childhood research--the Fisherian and the Neyman-Pearson models (both considered "classical" approaches), and the Bayesian model. The article concludes that all three models have a place in the analysis of research…

An approach to empirical Bayes analysis of aggregated survival data from different groups of subjects is presented based on a contingency table representation of data using transformations to permit the use of normal priors. Analysis of families of survival curves leads to improvements over classical estimates. (SLD)

Extended the use of a beta prior in trait estimation to the maximum expected a posteriori (MAP) method of Bayesian estimation. This new method, essentially unbiased MAP, was compared with MAP, essentially unbiased expected a posteriori, weighted likelihood, and maximum-likelihood estimation methods. The new method significantly reduced bias in…

Proposes a procedure for empirical initialization of the trait (theta) estimator in adaptive testing that is based on the statistical relation between theta and background variables known prior to test administration. Illustrates the procedure for an adaptive version of a test from the Dutch General Aptitude Battery. (SLD)

Individual differences in response to a given treatment have been a longstanding interest in education. While many evaluation studies focus on average treatment effects (i.e., the effects of treatments on the levels of outcomes of interest), this paper additionally considers estimating the effects of treatments on the dispersion in outcomes.…