Multidimensional scaling: I. Theory and method

Multidimensional scaling can be considered as involving three basic steps. In the first step, a scale of comparative distances between all pairs of stimuli is obtained. This scale is analogous to the scale of stimuli obtained in the traditional paired comparisons methods. In this scale, however, instead of locating each stimulus-object on a given continuum, the distances between each pair of stimuli are located on a distance continuum. As in paired comparisons, the procedures for obtaining a scale of comparative distances leave the true zero point undetermined. Hence, a comparative distance is not a distance in the usual sense of the term, but is a distance minus an unknown constant. The second step involves estimating this unknown constant. When the unknown constant is obtained, the comparative distances can be converted into absolute distances. In the third step, the dimensionality of the psychological space necessary to account for these absolute distances is determined, and the projections of stimuli on axes of this space are obtained. A set of analytical procedures was developed for each of the three steps given above, including a least-squares solution for obtaining comparative distances by the complete method of triads, two practical methods for estimating the additive constant, and an extension of Young and Householder's Euclidean model to include procedures for obtaining the projections of stimuli on axes from fallible absolute distances.This study was carried out while the author was an Educational Testing Service Psychometric Fellow at Princeton University. The author expresses his appreciation to his thesis adviser, Dr. H. Gulliksen, for his guidance throughout the study and to Dr. B. F. Green, Jr., for valuable assistance on several of the derivations.     

Datamyte 900

The Datamyte 900 solid-state, hand-held data collector is described.     

COR V2: Teaching observational research with multimedia courseware

Courseware for Observational Research (COR Version 2) is an interactive multimedia program designed to teach the foundation of the scientific method: systematic observation. COR uses digital video with interactive coding to teach basic concepts, such as creating precise operational definitions; using frequency, interval, and duration coding; developing sampling strategies; and analyzing and interpreting data. Through lessons, a case study, and laboratory exercises, it gradually scaffolds students from teacher-directed learning into self-directed learning. The newest addition to COR is a case study in which students work collaboratively, using their own observations to make recommendations about a child’s disruptive behavior in an after-school program. Evaluations of the lessons showed that classes using COR received better grades on their field observations than did those using methods that are more traditional. Students’ confidence and knowledge increased as they moved through each section of the program.     

Scaling and Psychometrika: Spatial and alternative representations of similarity data

Progress over the past twenty-five years in the development and improvement of models for representation of similarity data is reviewed. The discussion includes comments on class, dimensional, ideal type, and dichotomous attribute representations of underlying similarity structures. Most of the theoretical research in the area appeared, and continues to appear, inPsychometrika.     

COR V2: teaching observational research with multimedia courseware.

Courseware for Observational Research (COR Version 2) is an interactive multimedia program designed to teach the foundation of the scientific method: systematic observation. COR uses digital video with interactive coding to teach basic concepts, such as creating precise operational definitions; using frequency, interval, and duration coding; developing sampling strategies; and analyzing and interpreting data. Through lessons, a case study, and laboratory exercises, it gradually scaffolds students from teacher-directed learning into self-directed learning. The newest addition to COR is a case study in which students work collaboratively, using their own observations to make recommendations about a child's disruptive behavior in an after-school program. Evaluations of the lessons showed that classes using COR received better grades on their field observations than did those using methods that are more traditional. Students' confidence and knowledge increased as they moved through each section of the program.     

A non-parametric test of correlation using rank orders within subgroups

Kendall's rank order test for association between two variables is generalized to the case where the total sample is made up of several subgroups and the data on one or both variables consist of the rank order within each subgroup. The test involves no assumptions concerning scales of measurement, shapes of distributions, or relative level of excellence or amount of variability of the different subgroups. Two empirical examples indicate that the normal approximation to the exact test of significance can be considered adequate for most practical situations. Special consideration is given to the case of tied ranks. If ties occur in but one variable within any given subgroup, only a slight modification in procedure is needed. Extensive ties in both variables within subgroups lead to difficulties in determining the appropriate correction for continuity.