The results of an algorithm which is designed to take a set of commonality coefficients, either real or manipulated, and, if possible, produce one or more sets of regressor correlations that are consistent with them are examined. A number of different ways of resolving the higher order commonality values into their lower orders were tried and the…

In this paper 12 blind transformation procedures are applied to 18 data sets. The results of the analyses indicate that the orthotran transformation solution is not restricted to particular types of data as are so many other transformation solutions. The evidence presented in this paper strongly suggests that the orthotran solution must be…

Subjects are asked to answer six questions, partly with a frequency and partly by marking a verbally anchored scale with five categories. Some univariate and multivariate analyses are performed to elucidate the relations between variables with the two different modes of response. Although there are similarities in results for the two types of…

This study investigated middle school children's ability to form a mental image of a planar figure and to: (1) mentally flip, turn, or slide this representation and then construct the resultant image in correct position ("performing individual motions"), (2) perform two such motions in succession ("composition of motions"), (3) perform the process…

Under some circumstances, it is desirable to compare the factor patterns obtained from different factor analyses. To date, the best method of simultaneously achieving simple structure and maximum similarity is the technique devised by Bloxom (1968). This technique simultaneously rotates different factor patterns to maximum similarity and varimax…

This extension of Harris' classification system permits classification of the interval-scale properties of any 2 x 2 (two person, two choice) game. The system is compared to taxonomies developed by various previous researchers. It is shown to permit compact description of any 2 x 2 game as an octet of numbers. It also permits rapid classification…

Aitkin's generalized least squares (GLS) principle, with the inverse of the observed variance-covariance matrix as a weight matrix, is applied to estimate the factor analysis model in the exploratory (unrestricted) case. It is shown that the GLS estimates are scale free and asymptotically efficient. The estimates are computed by a rapidly…

This study compares the postulational approach to tenth grade geometry by three textbooks: one synthetic, one transformational, and one vectional. The development of incidence, order, distance, separation, congruence, parallelism, and similarity are discussed, and the different approaches illustrated. Special consideration is given to theorems in…

This document consists of unrevised lecture notes for the first half of a 20-week in-house graduate course at Rand Corporation. The chapter headings are: (1) Histograms and descriptive statistics; (2) Measures of dispersion, distance and goodness of fit; (3) Using JOSS for data analysis; (4) Binomial distribution and normal approximation; (5)…

The subjective magnitude estimation (SME) procedure was used to obtain estimates of relative word frequency from two adult groups (15 lexicographers, 13 other adults) for 60 words ranging widely in objective frequency. Lexicographers rendered more reliable estimates, and their averaged data correlated more highly with objective log frequency than…

The elementary school teacher's need for experience with geometry is described, and a series of topics which might be used in mathematics courses for elementary school teachers is offered. (SD)

The target point for the cue ball in a simplified game of billiards is computed through the use of line reflections and computations with complex numbers. (JT)

Discusses the principle elements for understanding and using mathematics, particularly arithmetic. Three aspects of arithmetic are considered: Understanding the concepts underlying a mathematical process, techniques or algorithms of arithmetic, and applications of the techniques to real situations. (SH)

Children aged four through eight performed a series of tasks involving two-dimensional isometrics to determine the amount of compatability between a mathematically-based organization of Euclidean transformation concepts and the existing cognitive structures of the children. Results confirmed that mathematical and cognitive structures are not…

An application of transformation geometry to special relativity is described. No knowledge of physics is required, but the application uses transformation ideas in a nontrivial way. A comparison is given of reflections in the Euclidean and Minkowski (non-Euclidean) planes. (MNS)