This paper illustrates the transformation of a raw data matrix into a matrix of associations, and then into a factor matrix. Factor analysis attempts to distill the most important relationships among a set of variables, thereby permitting some theoretical simplification. In this heuristic data, a correlation matrix was derived to display…

Order Analysis is a multidimensional scaling (MDS) technique for determining order among items. This paper reviews articles by different authors describing various components of ordering theory. A common nomenclature is constructed to link together the various ideas and is applied to a fairly simple set of data. Topics discussed include a more…

Despite advances in common factor analysis, a review of 89 studies published in four selected journals between 1963 and 1976 indicated that behavioral scientists preferred principal components analysis, followed by varimax or orthogonal rotation. Resultant row sums of squares of factor matrices from principal component analyses of real data sets…

This paper is an extended series of appendices to the report "Exploring the T.R.Q.: An Assessment of the Effectiveness of the Teachers' Rating Questionnaire," Report Number 123. It should be most useful to those familiar with multiple regression analysis and factor analysis and wishing a more complex record of the statistical procedures…

Confirmatory factor analysis was used to test first- and second-order factor models on cognitive abilities and their invariance across samples of 234 male and 225 female secondary school students. Factor models suggest that males and females may use different problem-solving strategies for spatial analogies, matrices, and numerical problems. (SLD)

In order to determine the effectiveness of multidimensional scaling (MDS) in recovering the dimensionality of a set of dichotomously-scored items, data were simulated in one, two, and three dimensions for a variety of correlations with the underlying latent trait. Similarity matrices were constructed from these data using three margin-sensitive…

Attitude measures frequently produce distributions of item scores that attenuate interitem correlations and thus also distort findings regarding the factor structure underlying the items. An actual data set involving 260 adult subjects' responses to 55 items on the Love Relationships Scale is employed to illustrate empirical methods for…

Any theory of information processing must address both what is processed and how that processing takes place. Most studies investigating variables which alter physical dimension utilization have ignored the large individual differences in selective attention or cue utilization. A paradigm was developed using an individual focus on information…

Geometric approaches to representing interrelations among tests and items are compared with an additive tree model (ATM), using 2,644 examinees and 2 other data sets. The ATM's close fit to the data and its coherence of presentation indicate that it is the best means of representing tests and items. (TJH)

While educational researchers frequently collect data from a sample of individuals on a sample of variables, they sometimes collect data involving samples of: (1) subjects; (2) variables; and (3) occasions of measurement. A multistage procedure for analyzing such three-mode data is presented, focusing on effect sizes and graphic confidence…

Six separate studies were conducted using judgments from academic and practitioner experts to determine the knowledge structure of the Certified Financial Planner Professional Education Program (i.e., the organization of discipline topics and the relationships among them). The program consists of six sequential financial planning knowledge…

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 VARAN (variance Analysis) program is an addition to a series of computer programs for multivariate analysis of variance. The development of VARAN exploits the full linear model. Analysis of variance, univariate and multivariate, is the program's main target. Correlation analysis of all types is available with printout in the vernacular of…

A scaling procedure is proposed, based on item response theory (IRT), to fit non-hierarchical test structure as well. The binary scores of a test of English were used for calculating the probabilities of answering each item correctly. The probability matrix was factor analyzed, and the difficulty intervals or estimates corresponding to the factors…

The construct validity of 14 measures used in college faculty personnel decisions was evaluated through a multitrait-multimethod matrix for data from 89 faculty members in 7 departments. The three-pronged model of teaching, research, and service was not validated. Exploratory factor analysis identified five or six behavior domains for evaluation.…