The empirical Bayes modeling approach--latent ability random sampling in the item response theory (IRT) context--to the IRT modeling of psychological tests is described. Under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test.…

In 1955, R. Levine introduced two linear equating procedures for the common-item non-equivalent populations design. His procedures make the same assumptions about true scores; they differ in terms of the nature of the equating function used. In this paper, two parameterizations of a classical congeneric model are introduced to model the variables…

A statistical procedure is presented that is designed to test for unidirectional test bias existing simultaneously in several items of an ability test, based on the assumption that test bias is incipient within the two groups' ability differences. The proposed procedure--Simultaneous Item Bias (SIB)--is based on a multidimensional item response…

Combining student scores to form subtotals and finally a total score to determine a grade is discussed. The composite score reached by combining measures or subtotals is only valid when the scores are combined so that the actual weight of each measure or subtotal in the total score is the same as the intended weight. Three types of variability…

The extent to which standardized regression coefficients (beta values) can be used to determine the importance of a variable in an equation was explored. The beta value and the part correlation coefficient--also called the semi-partial correlation coefficient and reported in squared form as the incremental "r squared"--were compared for…

An adaptive test can usually match or exceed the measurement precision of conventional tests several times its length. This increased efficiency is not without costs, however, as the models underlying adaptive testing make strong assumptions about examinees and items. Most troublesome is the assumption that item pools are unidimensional. Truly…

Item response theory (IRT) has proven to be a very powerful and useful measurement tool. However, most of the IRT models that have been proposed, and all of the models commonly used, require the assumption of unidimensionality, which prevents their application to a wide range of tests. The few models that have been proposed for use with…

In previous research, no relationship was found between test factor structure and test hierarchical structure. This study found some correspondence between test factor structure and test inter-item dependency structure, as measured by a log-linear model. There was an inconsistency, however, which warrants further study: more significant two-item…

Investigation of the effects of a series of treatment conditions upon some social behaviors may require observation of subjects mutually paired, in round-robin fashion. Data arising from such experiments are difficult to analyze, partly because they do not fit neatly into standard designs. A model is presented. (Author/BJG)

In applied and experimental research, it has been demonstrated that the extreme groups procedure is more powerful than the standard correlational approach for some values of the correlation and extreme group size. Methods are provided for using the covariance information that is usually discarded in the classical extreme groups approach.…

A course in differential equations for mathematics and physics students is designed to encourage students to models of situations in the sciences. (SD)

Proposes an enhanced approach to teaching topics in ecology--an approach that uses mathematical models and A Programming Language (APL) to produce short, quickly comprehensible computer "programs" that can be run to allow students to study the behavior of a particular model. (Author/IRT)

A numerical solution of the three-dimensional steady-state diffusion equation for a finite width line source is presented. The wind speed and eddy diffusivity as a function of height above the roadway are obtained. Normalized ground level and elevated concentrations near a highway are obtained for winds perpendicular, parallel, and at 45 degrees.…

Computer analysis of linguistic models leads the author to state that highly controlled transient memory should be considered in studies of the learning and use of grammar. (SD)