In many large-scale educational assessments it is of interest to compare the distribution of latent abilities of different subpopulations, and track these distributions over time to monitor educational progress. B. Junker, together with two colleagues, has developed a simple scheme, based on the proportion correct score, for smoothly approximating…

Multivariate methods are being used with increasing frequency in educational research because these methods control "experimentwise" error rate inflation, and because the methods best honor the nature of the reality to which the researcher wishes to generalize. This paper: explains the basic logic of canonical analysis; illustrates that…

Model justified the expectation that the transfer from learning one task to another is linearly dependent on the coefficient of intercorrelation between the two studies when the coefficient was corrected for attenuation. Supportive studies are cited. Regression curves yielded negative intercepts. Testable explanations were offered. (Author/BJG)

The fundamental results of integration theory are shown to follow from an axiomatic definition of the integral as a real valued function whose domain is a subset of the set of real valued functions of a real variable. (SD)

Geometric analysis of a cube can motivate formulae for factoring algebraic expressions involving sums and differences of cubes. (SD)

A network model is developed to determine the optimum number of shelf heights to use which will minimize the shelving cost for a given collection of books. (Author)

The mathematical theory of measurement is used to construct a framework for the evaluation of information retrieval strategies. (Author)

A mathematical model is given for predicting the growth of a card catalog and planning card redistribution. (PF)

The probability integral of the multivariate normal distribution (ND) has received considerable attention since W. F. Sheppard's (1900) and K. Pearson's (1901) seminal work on the bivariate ND. This paper evaluates the formula that represents the "n x n" correlation matrix of the "chi(sub i)" and the standardized multivariate…

The use of a Bayesian approach in evaluating data from clinical trials with many treatment centers and from many studies is discussed. The main distinction between a metaanalysis and an analysis of a multicenter trial is that different studies may have very different designs, while the centers in a multicenter trial usually follow the same…

Given that the examinee knows the answer to item i if and only if he knows the answer to both item g and item h, a "conjunctive" item response model is found such that items g, h, and i all have the same mathematical form of response function. Since such items may occur in practice, it is desirable that item response models satisfy this…

This study is an attempt to answer the following research question: can the reliability of a criterion-referenced test be accurately determined according to a multiple classification of the student's performance? Specifically, the study pursues the beta-multinomial model, which postulates the probability distribution of an examinee's degree of…

This document consists of three papers. The first, "A Parallel Model of (Sequential) Problem Solving," describes a parallel model designed to solve a class of relatively simple problems from elementary physics and discusses implications for models of problem-solving in general. It is shown that one of the most salient features of problem…

Rasch models for fundamental measurement in the psychological sciences are derived from the principle of specific objectivity, the requirement that the parameter value representing each component in a test situation be independent of the other components. The dichotomous Rasch model for two-faceted analysis, applicable to conventional…