Separability and Independence of Dimensions within the Same–Different Judgment Task

Abstract Ashby, Townsend, and colleagues have developed an important model for the psychophysical identification task, the general recog- nition theory (also called, decision bound theory), based on multi- dimensional signal detection theory, that has been extended to categorization, Garner filtering, similarity judgments, and preference successfully. The virtue of this theory (and its extensions) is the ability to assess the nature of the perceptual representations of stimuli (e.g., their dimensional interactions), within a single framework and across paradigms. This paper adds to this ability by extending the theory, and related multidimensional perceptual models, to the problem of same–different judgments. Three tasks are described for the example of two-dimensional stimuli. In two of these tasks only one dimension is relevant ( component same–different ). In the third, both dimensions are deemed relevant ( standard same–different ). Several theorems concerning both response accuracy and response time have been proved relating the property of perceptual separability to certain response time invariances that can be observed in the component same–different tasks. This property, generally speaking, is the constancy of perception of one dimension when another irrelevant dimension changes in the stimulus. Also, under the assumption of within-trial perceptual indepen- dence, response probabilities, and response times of the two–component tasks can be meaningfully related to those same measures in the standard same–different paradigm, provided motor time variance is minimal.