Through a series of six guided classroom discoveries, students create, via targeted questions, a definition for deciding when two sets have the same cardinality. The program begins by developing basic facts about cardinalities of finite sets. Extending two of these facts to infinite sets yields two statements on comparing infinite cardinalities…

The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data matrices. These examples are believed to be local…

Several methodological issues in the multidimensional scaling of coarse dissimilarities were studied, examining whether it was better to scale dissimilarity data directly or to scale a new matrix derived from the original by row comparisons. Findings support an alternative row-comparison measure based on the Jacard coefficient. (SLD)

Monte Carlo procedures were used to investigate the properties of a nonmetric multidimensional scaling algorithm when used to scale an incomplete matrix of dissimilarities. Recommendations for users wishing to scale incomplete matrices are made. (Author/RC)

This study was undertaken to compare non-metric multidimensional scaling (MDS) and factor analysis (FA) as means of assessing dimensionality in relation to item response theory (IRT). FA assesses correlation matrices, while MDS performs an analysis of proximity measures. Seven data sets were generated; each differed from the others with respect to…

Six major problems confronting attempts to use nonmetric multidimensional scaling to represent structures underlying similarity data are identified and the author's prospects for over-coming each of these problems are presented. (RC)

Three approaches to the graphic representation of similarity and dissimilarity matrices are compared and contrasted. Specifically, Kruskal's multidimensional scaling, Johnson's hierarchical clustering, and Waern's graphing techniques are employed to depict, in two dimensions, data representing the structure of a set of botanical concepts. Each of…

Procedures for analyzing common item effects on interscale structure were reviewed and a study using smallest space analysis of the California Psychological Inventory (CPI) reported. Solutions of three matrices--intercorrelation matrix of the original CPI scales, of reduced scales (with common items removed), and of the number of common…

Examines the similarity between the coordinates which resulted when correlations were used as similarity measures and the factor loadings obtained by factor analyzing the same correlation matrix. Real data, a set of error free data, and some computer generated data containing deliberately introduced sampling error are analyzed. (RC)

Two sets of real sorting data from 50 college students are used to compare results of multidimensional scaling of raw co-occurrence frequencies or dissimilarity measures (D) and profile distances (delta) to determine which yields a better representation of the underlying structure of 2 sets of stimuli. Slight differences are discussed. (SLD)

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)

This article's goals are to validate the Computer and Information Technology Attitude Inventory (Weinsier and Leutner, 1988), a nontraditional approach to attitude measurement; and to report on a study designed to search for intercultural differences or cross-cultural consistency of attitudes toward computers and information technology. (46…