Although perfectly scalable items rarely occur in practice, Guttman's concept of a scale has proved to be valuable to the development of measurement theory. If the score distribution is uniform and there is an equal number of items at each difficulty level, both the elements and the eigenvalues of the Pearson correlation matrix of dichotomous…

This paper discusses the use of latent class structure as a modelling framework for tests in which much of the data conforms to a relatively small number of systematic patterns. Application of this framework to the analysis of tests has been limited because available parameter estimation algorithms can only handle a relatively small number of…

Hypothetical data sets are used to demonstrate how canonical correlation methods subsume other commonly utilized parametric methods. Analysis of variance, analysis of covariance, multiple analysis of variance, and multiple analysis of covariance are heavily used by educational researchers. It is concluded that researchers would do well to consider…

Three item response models were evaluated for estimating item parameters and equating test scores. The models, which approximated the traditional three-parameter model, included: (1) the Rasch one-parameter model, operationalized in the BICAL computer program; (2) an approximate three-parameter logistic model based on coarse group data divided…

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical manifest variables. Two types of correlation matrices were analyzed; one containing Pearson product-moment correlations and one containing tetrachoric,…

A primary goal of this study was to determine the extent to which item difficulty was related to item position and, if a significant relationship was found, to suggest adjustments to predicted item difficulty that reflect differences in item position. Item response data from the Medical College Admission Test (MCAT) were analyzed. A data set was…

Analytical techniques used in responding to a series of four substantial budget reductions imposed at Oregon State University are described. Over a 2-year period, each of the budget reductions demanded increasingly severe institutional action to meet the specified monetary targets. Different analytical techniques were required to meet the changing…

The central purpose of the present study was to evaluate several statistical techniques (analysis of variance (ANOVA) on raw gains, standardized ANOVA, standard analysis of covariance (ANCOVA), and z-score ANOVA) under various quasi-experimental conditions (three levels of reliability, three levels of sample size, three levels of gain, and the…

A method is proposed to equate different sets of items administered to different groups of individuals using the Rasch model. A Rasch equating model was formulated to describe one common Rasch scale in different groups with different but overlapping sets of items. The item parameters can then be estimated simultaneously, avoiding different…

The use of confirmatory factor analytic procedures to examine the dimensionality of writing skills as measured by a large-scale direct writing test was illustrated. Internal construct validity evidence about the nature of writing skills measured by the test was provided. Data used were scores assigned by about 100 trained professional raters on a…

The focus of this study is on the estimation procedures implemented in BILOG, a computer program. One purpose is to compare the item parameter estimates produced by various procedures available in BILOG. Four different models are used: the one, two, and three parameter model and a three parameter model with common guessing parameters. The results…

This paper addresses the information revealed in incorrect option selection on multiple choice items. Multilinear Formula Scoring (MFS), a theory providing methods for solving psychological measurement problems of long standing, is first used to estimate option characteristic curves for the Armed Services Vocational Aptitude Battery Arithmetic…

This study investigated the feasibility of the use of the three-parameter item response theory (IRT) model in Florida's minimum competency testing program. The paper includes the following sections: (1) a description of the procedures currently being used by the assessment program, with an emphasis on procedures currently involving the Rasch…

Covariance structure modelling is applied to the problem of estimating reliability and measurement error in survey data. To provide a basis for grouping certain question or variable types (data from questions), a simple typology based on the formal characteristics of the questions is outlined. From this classification, models for the different…

This unit views applications of elementary game theory to international relations. It is noted that of all the significant world problems, the nuclear arms race has proved one of the most intractable. The main concern of the module is to investigate a possible solution to the arms race, based on extending the classic two-person game of Prisoner's…