To assess the effects of correlated abilities on test characteristics, and to explore the effects of correlated abilities on the use of a multidimensional item response theory model which does not explicitly account for such a correlation, two tests were constructed. One had two relatively unidimensional subsets of items, the other had all…

This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.

A method of estimating the operating characteristics of a new test item added to an established test without assuming a prior model has been proposed by the author. In this paper, the author extends this logic by proposing a different hypothesized distribution of the resulting estimate. The former method used a normal approximation; the present…

Five comparisons were made relative to the quality of estimates of ability parameters and item calibrations obtained from the one-parameter and three-parameter logistic models. The results indicate: (1) The three-parameter model fit the test data better in all cases than did the one-parameter model. For simulation data sets, multi-factor data were…

False-positive and false-negative dicisions are the fundamental errors committed with a mastery test; yet the estimation of the likelihood of committing these errors has not been investigated. Accordingly, two methods of estimating the likelihood of committing these errors are described and then investigated using Monte Carlo techniques.…

The number and diversity of the parameters involved in the organization of modern education make it necessary to employ modern management methods and techniques to optimize decisions about the organization and improve the use of available material and financial resources. To accomplish these goals, a systems approach is advisable. A model of any…

This paper presents and illustrates a technique that can be used to analyze the internal and external influences on community college enrollment trends and staffing patterns in a way that quantitatively expresses the amount of increase or decrease attributable to various competing factors. Introductory material relates the rationale behind the…

These modules develop two prevalent explanations among political scientists of who gets what in the budgetary process. Specifically, the problem of how an agency's level of appropriations changes over time is addressed. It is noted that budgeting is a political process in the classic sense, in that it elicits and embodies patterns of conflict and…

This module is designed for students with a high school algebra background. The goal is to present the elements of the group idea, primarily by way of a geometric model, and to see its application to the study of kinship relations within certain human groups. The material opens with a presentation of clans in a hypothetical society in an early…

One of the great strengths of mathematics is viewed as the fact that apparently diverse real-world questions translate into that same mathematical question. It is felt that studying a mathematical problem can often bring about a tool of surprisingly diverse usability. The module is geared to help users know how to use graph theory to model simple…

This document includes three units on applications of first-order difference equations to American politics. The first module is designed to help the user: 1) develop flexibility in analyzing difference equations in quadratic format; 2) understand how Choundy and Phillips' Theorem can be used to provide information about the time path of a…

A large-scale and a small-scale simulation of the reallocation of students into and out of an originally-selected treatment group were performed. It was postulated that both the scores on a selection test and teacher ratings are measures of student needs in the Title I Evaluation and Reporting System (TIERS). In the norm-referenced model, three…

To test whether equity in educational expenditure can include equity for taxpayers, the authors analyze two suggested methods for achieving educational equity. The two methods are district power equalizing (DPE), which grants state aid in inverse proportion to school district wealth, and the wealth neutral system (WNS), which takes account of…

This paper describes an analytical solution to a common problem in aptitude-treatment interaction (ATI). The researcher is often interested in the comparison between treatments for a large set of attributes. If this set is large, the chance of non-orthogonality is correspondingly large. In these circumstances the analysis and interpretation…

This case study describes the application of an analytical library network model to data collected during April 1977. Models are developed for describing the intralibrary processing activities encountered at each of the resource libraries in the study, and alternative routing policies for referring requests among resource libraries are analyzed. A…