Recent work in factor analysis of categorical variables is reviewed, emphasizing a generalized least squares solution and a maximum likelihood approach. A common factor model for dichotomous items is introduced, and the estimation of factor loadings from matrices of tetracorrelations is discussed. (LMO)

Reports on Commonwealth Scientific and Industrial Research Organization (Australia) efforts to establish library staffing standards by use of statistics on current library operations and comparison of figures for number of libraries. Research methodology, use of mathematical models, factor analysis and regression analysis, and measures of…

A mathematical model is proposed to describe how group differences in distributions of abilities, which are distinct from the target ability, influence the probability of a correct item response. In the multidimensional approach, differential item functioning is considered a function of the educational histories of the examinees. (SLD)

The purposes of this study are to examine the factorial invariance of responses by preadolescent males and females to a multidimensional self-concept instrument, and to demonstrate the use of confirmatory factor analysis (CFA). Sets of responses by 500 males and by 500 females were each randomly divided in half to form four groups (M1, M2, F1, and…

The Joreskog and Sorbom LISREL (linear structural relations) method is investigated as an alternative to regression analysis in studies of aptitude-treatment interactions (ATI), to solve problems caused by unreliability of measurements and by large sets of variables. A study reported by M.J. Behr is reanalyzed. This study investigated relations…

Failure to consider errors of measurement when using partial correlation or analysis of covariance techniques can result in erroneous conclusions. Certain aspects of this problem are discussed and particular attention is given to issues raised in a recent article by Brewar, Campbell, and Crano. (Author)

Statistical procedures are presented for determining ordinal and disordinal aptitude-treatment interactions with linear and curvilinear data. The paper presents a method for testing the homogeneity of group regressions for a single aptitude and provides models for expanding this test to linear and curvilinear regression planes. Procedures are…

Issues related to between-class and within-class decomposition of achievement variance and the change of this decomposition over the course of the eighth-grade were examined using the Second International Mathematics Study (SIMS, 1985), a study in which there was a nested or hierarchical data structure of students within classes, within schools,…

The adequacy of several approaches to estimation of proficiency distributions for the Trial State Assessment (TSA) in eighth grade mathematics of the National Assessment of Educational Progress was examined. These approaches are more restrictive than the estimation procedures originally used, with the same kind of plausible-values approach that…

When the three-parameter logistic model and item response theory are used to analyze Graduate Management Admission Test (GMAT) data, there are problems with the assumption of unidimensionality. Linear factor analytic models, exploratory factor analysis programs, and the comparison of item parameter estimates for heterogeneous and homogeneous…

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…

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…

Three methods of item selection were used to select sets of 38 items from a 50-item verbal analogies test and the resulting item sets were compared for internal consistency, standard errors of measurement, item difficulty, biserial item-test correlations, and relative efficiency. Three groups of 1,500 cases each were used for item selection. First…