SIMILARITY AND THE DENSITY HYPOTHESIS

Similarity data may show certain patterns, such as asymmetries and variations in similarity with changes in context set, that are inconsistent with traditional geometric models of similarity. Krumhansl (1978) suggested that these effects could be explained by an extension of the traditional Euclidean geometric model that she termed the distance-density model. The central assumption of the distance-density model is the density hypothesis, which states that the psychological similarity between two objects, x and y, is a function not only of the distance between them in the geometric attribute space, but also of the density of other objects in the space in the regions of x and y. The density hypothesis proposes that similarity is a decreasing function of these density components.

Three studies sought to test the density hypothesis for similarity ratings of pairs of simple geometric figures. Density was manipulated for particular stimuli in a between-subjects design, and the effect on the similarity ratings in each condition was measured. In each of the studies there was no significant relation of density to rated similarity.

Three further studies sought to confirm or reject the existence of a density effect for confusions among letters and letter-like stimuli. In a discrimination task using letter-like figures, the manipulation of density significantly affected confusion probabilities, but the direction of the effect was opposite to that predicted by the density hypothesis. In another discrimination task that manipulated density by choosing different subsets of actual letter stimuli, there was no significant effect of density on confusion probability. In a fatal experiment, that examined errors in letter identification under degraded conditions, there was a marginally significant relationship between density and confusions probability. However, asymmetric confusion probabilities in the data were not well predicted by a density measure.