Spatial metrics of integral and separable dimensions

Conducted 2 experiments with 24 undergraduates to investigate the relationship between dimensional integrality and the form of the combination rule or spatial metric used in a similarity judgment task. In Exp I, 2 groups judged the dissimilarity of all pairwise combinations of 12 rectangles differing in height and width (integral dimensions) or 12 circles differing in size and diameter (separable dimensions). The dimensional organization and spatial metric of both sets of dimensions were determined. Results show that differences in height and width contributed independently to judgments of the overall dissimilarity of rectangles and that these dimensions were combined using a Euclidean metric. In contrast, substantial interactions between circle size and diameter orientation were found. Combinations also appeared to violate the triangle inequality implying that no spatial metric was appropriate. In Exp II, parallelogram size and tilt were analyzed. Although some degree of dimensional interaction was observed, it was found that on the average these dimensions were combined using a city-block metric. In a subsequent speeded classification task, orthogonal interference was observed, which suggested that size and tilt are integral dimensions. The implications for the supposed association between the Euclidean metric and dimensional integrality are discussed. (36 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved).