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 , between two multivariate stimuli. In recent attempts to assess perceptual representations using qualitative tests on response probabilities, the concept of ad′ between two multidimensional stimuli has played a central role. For example, Kadlec and Townsend (1992a, 1992b) proposed several tests based on multidimensional signal detection theory that allow conclusions concerning the perceptual and/or decisional interactions of stimulus dimensions. One proposition, referred to as thediagonal d′test, relies on specific stimulus subsets of a feature-complete factorial identification task to infer perceptual separability. Also, Ashby and Townsend (1986), in a similar manner, attempted to relate perceptual independence to dimensional orthogonality in Tanner’s (1956) model, which also involvesd′ between two multivariate signals. An analysis of the proposedd′ _g reveals shortcomings in the diagonald′ test and also demonstrates that the assumptions behind equating perceptual independence to dimensional orthogonality are too weak. Thisd′ _g can be related to a common measure of statistical distance, Mahalanobis distance, in the special case of equal covariance matrices.