Dimensional models for the perception of rectangles.

Abstract

Krantz and Tversky (1975), Takane (1981), Wender (1971), and others have suggested that it is impossible to explain similarity judgments for rectangles by a simple dimensional model of the Minkowski distance type, because the psychologically compelling dimensions are not independent and interact. For reasons never made explicit, the relevant dimensions were assumed to be area and shape, rather than width and height. Reanalyses show, however, that the latter dimensions, appropriately scaled, eliminate interaction effects. To test these conclusions empirically, an experiment was carried out with two sets of rectangles. Each set was a complete 4×4 design, one in width × height coordinates, and one in area × shape coordinates. For each stimulus set, 21 subjects judged the dissimilarities of all pairs of rectangles twice. All subjects were reliable. Apart from one extreme subject in each group, all data lead to very similar MDS solutions. These solutions correspond closely to the predictions, that is, they can be well approximated with physical width and height coordinates rescaled such that the units decrease increasingly as one moves away from the origin. No interaction effects are found, but some indications for a more complicated composition rule are observed.