Two sets of five items each from the Law School Admission Test were analyzed by two methods of factor analysis, and by the Krus-Bart ordering theoretic method of multidimensional scaling. The results indicated a conceptual gap between latent trait theoretic procedures and order theoretic procedures. (Author/CTM)

A complete matrix formulation of the theory of small oscillations is presented. Simple analytic solutions involving matrix functions are found which clearly exhibit the transients, the damping factors, the Breit-Wigner form for resonances, etc. (BB)

Characteristics of liberal arts education and different approaches to educational modeling are examined. Attention is directed to: applications of graphic depictions; Venn-Euler diagrams to represent inclusion-exclusion phenomena as well as areas of commonality in learning processes and liberal education; the uses of flow charts for describing…

Simple continuity is applied with graph theory to generate a student flow model with multiple inputs and outputs. A graph of all semesters or nodes is laid out along with an input block for transfers in and an output block for transfers out. Arcs are connected from the zero node to the graduation node and these are placed in a time-forward…

This collection of materials includes six units dealing with applications of matrix methods. These are: 105-Food Service Management; 107-Markov Chains; 108-Electrical Circuits; 109-Food Service and Dietary Requirements; 111-Fixed Point and Absorbing Markov Chains; and 112-Analysis of Linear Circuits. The units contain exercises and model exams,…

This yearbook provides the mathematics education community with specific perceptions about discrete mathematics concerning its importance, its composition at various grade levels, and ideas about how to teach it. Many practical suggestions with respect to the implementation of a discrete mathematics school program are included. A unifying thread…

A basic structure approach is proposed for obtaining multidimensional scale values for attitude, achievement, or personality items from response data. The technique permits the unconfounding of scale values due to response bias and content and partitions item indices of popularity or difficulty among a number of relevant dimensions. (Author/BH)

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…

Two sets of real sorting data from 50 college students are used to compare results of multidimensional scaling of raw co-occurrence frequencies or dissimilarity measures (D) and profile distances (delta) to determine which yields a better representation of the underlying structure of 2 sets of stimuli. Slight differences are discussed. (SLD)

A general linear model (GLM), using least-squares techniques, was used to develop a criterion measure to replace freshman year grade point average (GPA) in college admission predictive validity studies. Problems with the use of GPA include those associated with the combination of grades from different courses and disciplines into a single measure,…

This study investigated the convergent validity of expert-system scores for four mathematical constructed-response item formats. A five-factor model was proposed comprised of four constructed-response format factors and a Graduate Record Examinations (GRE) General Test quantitative factor. Subjects were drawn from examinees taking a single form of…

This document consists of two modules. The first studies a variety of multicandidate voting systems, including approval, Borda, and cumulative voting, using a model which takes account of a voter's intensity of preference for candidates. The voter's optimal strategy is investigated for each voting system using decision criteria under uncertainty…

This unit, which looks at applications of linear algebra to population studies, is designed to help pupils: (1) understand an application of matrix algebra to the study of populations; (2) see how knowledge of eigen values and eigen vectors is useful in studying powers of matrices; and (3) be briefly exposed to some difficult but interesting…

Drawing on the authors' extensive experience at Stanford University as well as the work of others, this book offers the first systematic approach to fiscal and human resource planning at colleges and universities. It shows how decision models can and should become an integral part of the planning process. The uses and misuses of planning models in…

Various methods used to assess the content of a test are reviewed, and a new procedure designed to improve on these methods is presented. The two tests considered are a professional licensure examination, the auditing section of the Uniform Certified Public Accountant Examination, and an educational achievement test, a nationally standardized…