Assessing sensitivity in a multidimensional space: Some problems and a definition of a general d '

This article provides a formal definition for a sensivity measure, d(g)', b etween two multivariate stimuli. In recent attempts to assess perceptual re presentations using qualitative tests on response probabilities, the concep t of a d' between two multidimensional stimuli has played a central role. F or example, Kadlec and Townsend (1992a, 1992b) proposed several tests based on multidimensional signal detection theory that allow conclusions concern ing the perceptual and/or decisional interactions of stimulus dimensions. O ne proposition, referred to as the diagonal d' test, relies on specific sti mulus subsets of a feature-complete factorial identification task to infer perceptual separability. Also, Ashby and Townsend (1986), in a similar mann er, attempted to relate perceptual independence to dimensional orthogonalit y in Tanner's (1956) model, which also involves d' between two multivariate signals. An analysis of the proposed d(g)' reveals shortcomings in the dia gonal d' test and also demonstrates that the assumptions behind equating pe rceptual independence to dimensional orthogonality are too weak. This d(g)' can be related to a common measure of statistical distance, Mahalanobis di stance, in the special case of equal covariance matrices.