Presents a review of fundamental concepts and applications used to address the Behrens-Fisher problem (W. Behrens, 1929 and R. Fisher, 1935), a problem in testing the difference between two population means, through fiducial, Bayesian, and frequentist approaches. (Contains 86 references.) (SLD)

It is not unusual for several tests measuring different abilities to be given in one test administration. A common practice is to estimate these abilities independently of each other, but this paper proposes a more efficient method of estimating these abilities that takes into account the correlational structure of the abilities. The method uses a…

Modern statistics are considered as a branch of psychometrics and the question of how the central problems of statistics can be resolved using psychometric methods is investigated. Methods developed in the fields of test theory, scaling, and factor analysis are related to principle problems of modern statistical theory and method. (Author/JKS)

Argues that selecting data according to expected information gain, as proposed by M. Oaksford and N. Chater (1994, 1996), leads to suboptimal performance in Bayesian hypothesis testing. Procedures are presented that are better justified normatively, their psychological implications are explored, and a number of novel predictions are derived under…

Argues that Klauer's proposal (1999) and proposal presented are equally well justified from a normative perspective and that, where the predictions of the two approaches diverge, the existing empirical evidence is consistent with the information gain approach. Recommends that more empirical research is required to decide between these two…

Experimental data on human reasoning in hypothesis-testing tasks is reassessed in light of a Bayesian model of optimal data selection in inductive hypothesis testing. The rational analysis provided by the model suggests that reasoning in such tasks may be rational rather than subject to systematic bias. (SLD)

Focusing on a single sample obtained randomly with replacement from a single population, this article examines the regression of population on sample proportions and develops an unbiased estimator of the square of the correlation between them. This estimator turns out to be the regression coefficient. Use of the squared-correlation estimator as a…

Several norms for how people should assess a question's usefulness have been proposed, notably Bayesian diagnosticity, information gain (mutual information), Kullback-Liebler distance, probability gain (error minimization), and impact (absolute change). Several probabilistic models of previous experiments on categorization, covariation assessment,…

This article explores the potential of Bayesian inference as a theoretical framework for describing how people evaluate hypotheses. First, it identifies a set of logically possible forms of non-Bayesian behavior. Second, it reviews existing research in a variety of areas to see whether these possibilities are ever realized. (Author/BW)

There are currently three main approaches to parameter estimation in item response theory (IRT): (1) joint maximum likelihood, exemplified by LOGIST, yielding maximum likelihood estimates; (2) marginal maximum likelihood, exemplified by BILOG, yielding maximum likelihood estimates of item parameters (ability parameters can be estimated…

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…

When using item response theory (IRT) models in educational and psychological measurement, it is standard practice to estimate the operating characteristics of test items from examinees' item responses alone. This is the final report of a project that employed Bayesian and empirical Bayesian methods to exploit additional information that is often…

A short review of the different estimation procedures that have been used in association with the Rasch model is provided. These procedures include joint, conditional, and marginal maximum likelihood methods; Bayesian methods; minimum chi-square methods; and paired comparison estimation. A comparison of the marginal maximum likelihood estimation…

Olae is a computer system for assessing student knowledge of physics, and Newtonian mechanics in particular, using performance data collected while students solve complex problems. Although originally designed as a stand-alone system, it has also been used as part of the Andes intelligent tutoring system. Like many other performance assessment…

Presents a method of modeling the relevance relationship in information retrieval to answer the question of the theoretical limits of certain statistical methods. Hypergeometric probability distribution is used to construct an abstract model of a database of MEDLINE records, and results of tests of vector retrieval methods are reported. (28…