Large sample standard errors of linear equating for the single-group design are derived without making the normality assumption. Two general methods based on the delta method of M. Kendall and A. Stuart (1977) are described. One method uses the exact partial derivatives, and the other uses numerical derivatives. Simulation using the beta-binomial…

Equating tests from different calibrations under item response theory (IRT) requires calculation of the slope and intercept of the appropriate linear transformation. Two methods have been proposed recently for equating graded response items under IRT, a test characteristic curve method and a minimum chi-square method. These two methods are…

A detailed investigation of the statistical procedure of W. Stout (the computer program DIMTEST) for testing the hypothesis that an essentially unidimensional latent trait model fits observed binary response data from a psychological test is presented. One finding is that DIMTEST may fail to perform as desired in the presence of guessing when…

The graded response model for two-stage testing was applied to an attitudes toward science scale using real-data simulation. The 48-item scale was administered to 920 students at a grade-8 equivalent in Singapore. A two-stage 16-item computerized adaptive test was developed. In two-stage testing an initial, or routing, test is followed by a…

The existence of differential prediction of two-year grade point average is reported for gender groups within programs of study at the University of Iowa. Academic records of all freshmen entering the University in 1978 in the fields of Business, Liberal Arts, Pre-Medicine, and those undecided as to major were analyzed with respect to American…

An interview protocol was devised to determine whether demands on working memory are reduced by the use of drawn or telegraphic formats. Students were chosen because some aspect of their group testing on presentation formats was provocative (e.g. high spatial score, but low reading comprehension score; high drawn score and low verbal score, etc.).…

This paper describes a quantitative model that can be used to evaluate faculty performance for promotion decisions. Through the use of an evaluation form, the system (1) informs faculty members how they will be evaluated at the end of each academic year; (2) allows faculty growth to be documented in teaching, research, and other activities which…

Activities and teaching methods for developing an understanding of fractions are presented. The activities, which use mathematical models (visual representations of fractions), are divided into three sections: (1) equivalent fraction circles; (2) fraction bars; and (3) multiplication of fractional numbers using squares. Each section includes the…

The primary task in solving a physics problem is to select ways of viewing the problem in terms of physical systems whose behavior is described by physical laws. The physical systems are, in general, only approximate models of the real-world systems. As models of real-world systems are made more accurate, the equations involved quickly become…

This volume is an exposition of a mathematical modeling technique for use in the evaluation and solution of complex educational problems at all levels. It explores in detail the application of simple algebraic techniques to such issues as program reduction, fiscal rollbacks, and computer curriculum planning. Part I ("Introduction to the…

This paper illustrates the transformation of a raw data matrix into a matrix of associations, and then into a factor matrix. Factor analysis attempts to distill the most important relationships among a set of variables, thereby permitting some theoretical simplification. In this heuristic data, a correlation matrix was derived to display…

Queuing theory is examined in this paper in order to determine if the theory could be applied in educational settings. It is defined as a form of operations research that uses mathematical formulas and/or computer simulation to study wait and congestion in a system and, through the study of these visible phenomena, to discover malfunctions within…

This paper discusses new psychometric analyses that improve capabilities for relating performance on achievement test items to instruction received by examinees. The modeling discussion is closely tied to data for eighth graders in the United States provided by the Second International Mathematics Study (SIMS), comprising not only responses to a…

A new method for estimating the parameters of the normal ogive three-parameter model for multiple-choice test items--the normalized direct (NDIR) procedure--is examined. The procedure is compared to a more commonly used estimation procedure, Lord's LOGIST, using computer simulations. The NDIR procedure uses the normalized (mid-percentile)…

This study compared five density estimation techniques applied to samples from a population of 272,244 examinees' ACT English Usage and Mathematics Usage raw scores. Unsmoothed frequencies, kernel method, negative hypergeometric, four-parameter beta compound binomial, and Cureton-Tukey methods were applied to 500 replications of random samples of…