A nominal response model-based computerized adaptive testing procedure (nominal CAT) was implemented using simulated data. Ability estimates from the nominal CAT were compared to those from a CAT based upon the three-parameter logistic model (3PL CAT). Furthermore, estimates from both CAT procedures were compared with the known true abilities used…

This publication presents teaching strategies to develop understanding of fractions as sensible numbers. Written for the mathematics teacher in grades K-5, it gives suggestions for teacher-led discussions and structured exploratory activities. The activities are conducted with manipulative materials that emphasize the important characteristics and…

This paper is part of a series of applied statistics monographs intended to provide supplementary reading for applied statistics students. In the present paper, derivations of the unbiased standard error of estimate for both the raw score and standard score linear models are presented. The derivations for raw score linear models are presented in…

Six editions of Scholastic Aptitude Test-Mathematical (SAT-M) were factor analyzed using confirmatory and exploratory methods. Confirmatory factor analyses (using the LISREL VI program) were conducted on correlation matrices among item parcels--sums of scores on a small subset of items. Item parcels were constructed to yield correlation matrices…

Factor analysis is the traditional method for studying the dimensionality of test data. However, under common conditions, the factor analysis of tetrachoric correlations does not recover the underlying structure of dichotomous data. The purpose of this paper is to demonstrate that the factor analyses of tetrachoric correlations is unlikely to…

Statistical methodologists have sometimes criticized the use of conventional statistics in meta-analysis, and in recent years a number of them have advocated the use of a special new statistical methodology for research synthesis. An examination of recent books describing this methodology shows that it is seriously limited in its applicability to…

This paper examines the pattern of diffusion in the academic literatures of the sciences, social sciences, and arts and humanities based on citations. An examination of the citations of articles in the Science Citation Index, Social Science Citation Index, and Arts and Humanities Citation Index from a given year to the year in which the cited…

This study examined how four commonly used test equating procedures (linear, equipercentile, Rasch Model, and three-parameter) would respond to situations in which the properties or the two tests being equated were different. Data for two tests plus an external anchor test were generated from a three parameter model in which mean test differences…

This is a critical review of the analytical models developed by the U.S. Army to predict training device effectiveness. The Simulation Systems Technical Area of the U.S. Army Research Institute for the Behavioral and Social Sciences performed the research. Special consideration is given to a family of models known collectively as TRAINVICE. These…

Classroom researchers are frequently urged to provide evidence of the reliability of their data. In the case of observational data, three approaches to this have emerged: observer agreement, generalizability theory, and measurement error. Generalizability theory provides the most powerful approach given an adequate data collection design, but…

This paper describes and illustrates a simulation model for the processing of grammatical elements in a sentence, focusing on one aspect of sentence comprehension: the assignment of the constituent elements of a sentence to the correct thematic case roles. The model addresses questions about sentence processing from a perspective very different…

In 1972, the Oregon State Department of Education changed its standards relating to graduation requirements after a survey revealed concern that the high school diploma had lost its credibility. Parkrose School District developed a goal-based curriculum and measurement program to meet the new requirements. From the program's inception, District…

This study introduced a probabilistic model utilizing item response theory (IRT) for dealing with a variety of misconceptions. The model can be used for evaluating the transition behavior of error types, advancement of learning stages, or the stability and persistence of particular misconceptions. Moreover, it apparently can be used for relating…

One aim of this report is to show and emphasize that in the computational approaches to most of today's pressing and challenging scientific and technological problems, the mathematical aspects cannot and should not be considered in isolation. Following an introductory chapter, chapter 2 discusses a number of typical problems leading to…

The purpose of this research study was to assess item response model-test data fit using residuals. First, a comparison of raw and standardized residuals for describing model-test data fit was carried out. Second, hypotheses concerning the relationship between residual sizes and several item characteristics were studied. The analyses with…