Dimensional and metric structures in multidimensional stimuli.

The present experiments investigated two characteristics of subjects' multidimensional representations: their dimensional organization and metric structure, for both analyzable and integral stimuli. In Experiment 1, subjects judged the dissimilarity between all pairs of stimuli differing in brightness and size (analyzable stimuli), while in Experiment 2, subjects made dissimilarity judgments for stimuli varying in width height, and area shape (integral stimuli). For the brightness size stimuli, the findings that (a) brightness judgments were independent of size (and vice versa) and (b) the best fitting scaling solution was one that depicted an orthogonal structure are strong evidence that subjects perceived brightness size as a dimensionally organized structure. In contrast, for the rectangle stimuli, neither width height nor area shape contributed additively to overall dissimilarity. The results of the metric fitting were more equivocal. For all stimulus sets, the Euclidean metric yielded scaling solutions with lower stress values than the city block metric. When bidimensional ratings were regressed on unidimensional ratings, the city block metric yielded a slightly higher correlation coefficient than the Euclidean metric for brightness size stimuli. The two rules of combination were equivalent for the width-height stimuli, but the Euclidean metric provided a better approximation for the area shape stimuli. The results were discussed in terms of how subjects integrate physical dimensions for the case of integral stimuli and the superiority of dimensional vs. metric structure as an indicator of stimulus analyzability.