The authors discuss empirically determined competence areas to K-12 computer science education, emphasizing the cognitive level of competence. The results of a questionnaire with 120 professors of computer science serve as a database. By using multi-dimensional scaling and cluster analysis, four competence areas to computer science education…

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…

The effects of nonnormally distributed perceived distance between pairs of objects on the accuracy of recovered configurations of traditional multidimensional scaling were studied via simulation methods. Multidimensional scaling is shown to be robust with respect to violations of the assumption of normality. (Author/JKS)

Relations between Tucker's three-mode multidimensional scaling and Carroll and Chang's INDSCAL are discussed. A technique to transform a three-mode solution to the general form of an INDSCAL solution along with applications to two sets of data from the literature are presented. (Author/JKS)

The geometric properties and Euclidean nature of dissimilarity coefficients defined on finite sets are discussed. Several particular transformations are presented that preserve Euclideanarity. The study of a one-parameter family adds to current knowledge of the metric and Euclidean structure of coefficients based on binary data. (SLD)

A strategy for reordering the hierarchical tree structure is presented. While the order of terminal nodes of Johnson's procedure is arbitrary, this procedure will rearrange every triad of nodes under a common least upper node so that the middle node is nonarbitrarily closest to the anchored node. (Author/CTM)

Based on a simple nonparametric procedure for comparing two proximity matrices (matrices which represent the similarities among a set of objects), a measure of concordance (agreement) is introduced that is appropriate when K independent proximity matrices are available. (Author/JKS)

The solution of weakly constrained regression problems typically requires the iterative search, in a given interval, of a point where a certain function has a zero derivative. This note deals with improved bounds for the interval to be searched. (Author)

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)

A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. Numerical examples were…

Three dissimilarity measures for the unconstrained sorting task are investigated. All three are metrics, but differ in the kind of compensation which they make for differences in the sizes of cells within sortings. Empirical tests of the measures are done with sorting data for occupations names and the names of behaviors, using multidimensional…

A FORTRAN computer program was derived for an IBM series 360/370 computer system that provides a factor analytic solution for large three-dimensional data matrices. The computational procedures employed are based upon those presented in Method III by Tucker. (Author/JKS)

Two least squares procedures for symmetrization of a conditional proximity matrix are derived. The solutions provide multiplicative constants for scaling the rows or columns of the matrix to maximize symmetry. (Author/JKS)