Multidimensional item difficulty (MID) is proposed as a means of describing test items which measure more than one ability. With mathematical story problems, for instance, both mathematical and verbal skills are required to obtain a correct answer. The proposed measure of MID is based upon three general assumptions: (1) the probability of…

This paper reports the results of a Monte Carlo investigation of Type I errors in the single group repeated measures design where multiple measures are collected from each observational unit at each measurement occasion. The Type I error of three multivariate tests were examined. These were the doubly multivariate F test, the multivariate mixed…

A Monte Carlo study of five indices of dimensionality of binary items used a computer model that allowed sampling of both items and people. Five parameters were systematically varied in a factorial design: (1) number of common factors from one to five; (2) number of items, including 20, 30, 40, and 60; (3) sample sizes of 125 and 500; (4) nearly…

The work presented in this paper defined conceptually the concepts of multidimensional discrimination and information, derived mathematical expressions for the concepts for a particular multidimensional item response theory (IRT) model, and applied the concepts to actual test data. Multidimensional discrimination was defined as a function of the…

Reading test data from the National Assessment of Educational Progress (NAEP) were scaled using the unidimensional item response theory model. Data were collected for students aged 9, 13, and 17. To determine whether the responses to the reading items were consistent with unidimensionality, four different methods were applied: (1) principal…

Approximately 1200 Danish school children aged 8, 11, and 14 participated in a questionnaire study under the caption, "Why I like to read." Data from Denmark formed part of an international study, in which 12 other countries used the same questionnaire to explore various functions of reading and to compare them over different countries.…

This investigation examined the influence of sample size on different goodness-of-fit indices used in confirmatory factor analysis (CFA). The first two data sets were derived from large normative samples of responses to a multidimensional self-concept instrument and to a multidimensional instrument used to assess students' evaluations of teaching…

After observing secondary school students having great difficulty learning geometry in their classes, Dutch educators Pierre van Hiele and Dina van Hiele-Geldof developed a theoretical model involving five levels of thought development in geometry. It is the purpose of this monograph to present English translations of some significant works of the…

The focus is on the formulation and solution of mathematical models with the idea of a population employed mainly as a pedogogical tool. If the biological setting is stripped away, the material can be interpreted as topics or the qualitative behavior of differential and difference equations. The first group of models investigate the dynamics of a…

The first four units cover aspects of medical applications of calculus: 71-Measuring Cardiac Output; 72-Prescribing Safe and Effective Dosage; 73-Epidemics; and 74-Tracer Methods in Permiability. All units include a set of exercises and answers to at least some of the problems. Unit 72 also contains a model exam and answers to this exam. The fifth…

Employers and school admissions officials must consider several factors when making choices among applicants, particularly when faced with a need to increase selection of minority group members. Should different standards be applied to different groups? Will acceptance of less qualified applicants from one group affect the overall quality of the…

A study was conducted to compare tailored testing procedures based on a Bayesian ability estimation technique and on a maximum likelihood ability estimation technique. The Bayesian tailored testing procedure selected items so as to minimize the posterior variance of the ability estimate distribution, while the maximum likelihood tailored testing…

The efficacy of employing subsets of items from a calibrated item pool to estimate the Rasch model person parameters was investigated. Specifically, the degree of invariance of Rasch model ability-parameter estimates was examined across differing collections of simulated items. The ability-parameter estimates were obtained from a simulation of…

Three test-analysis models were used to analyze three types of simulated test score data plus the results of eight achievement tests. Chi-square goodness-of-fit statistics were used to evaluate the appropriateness of the models to the four kinds of data. Data were generated to simulate the responses of 1,000 students to 36 pseudo-items by…

Alternative mathematical models for scoring and decision making with criterion referenced tests are described, especially as they concern appropriate test length and methods of establishing statistically valid cutting scores. Several of these approaches are reviewed and compared on formal-analytic and empirical grounds: (1) Block's approach to…