Quantitative judgments of color: The square root rule

Judgments of the appearance of colored papers blended with different proportions of white were obtained using a rotating color mixer. Responses consisted of a mark on a line labeled with the appropriate color name at one end and “white” at the other. Prior context was avoided by obtaining only single judgments. It was found for all six color displays that distance from the colored end of the line was proportional to the square root of the proportion of white present in the mixture. This square root relation is in keeping with the physical correlate theory and with other experiments involving gray papers, point sources, and luminous fields.     

Lightness of grays: Effects of Background reflectance

The influence of background reflectance was determined for lightness judgments relative to white of small gray patches. The effect of prior stimulus-context was avoided by considering only first judgments. It was found that lightness was proportional to the square root of reflectance when the background was a gray darker than the stimulus, but not when the background was lighter gray or white. In general, a small difference in reflectance between the stimulus and and background produced the same effect as a larger difference.     

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.     

An appraisal of the validity of the factor loadings employed in the construction of the primary social attitude scales

In this article the authors examine the effect of including alternate test forms in a factor matrix upon the validity of the resultant factor loadings, finding that in this particular instance the effect is negligible. Comparisons of the factor loadings derived from matrices in which only one of the alternate test forms is included with those in which both forms are included reveal practically no difference in the magnitude of either the original or rotated factor loadings, or in that of the computed communalities.