Diagonal d′ does not (always) diagnose failure of separability: An addendum to Kingston, Diehl, Kirk, and Castleman (2008)

Kingston, Diehl, Kirk, and Castleman [Kingston, J., Diehl, R. L., Kirk, C. J., Castleman, W.A., 2008. On the perceptual structure of distinctive features: The [voice] contrast. Journal of Phonetics, 36, 28-54] present a sophisticated experimental design and detection theoretic analysis of the internal auditory structure of phonological contrasts. However, a potentially important aspect of multidimensional detection theory-the covariance structure of assumed underlying multivariate Gaussian perceptual densities-was left unexplored. We discuss Kingston et al.'s approach in the context of a general definition of multidimensional d′ and present a description of two distinct configurations of perceptual densities requiring fundamentally different interpretations that account equally well for the “mean-shift integrality” results reported by Kingston et al. We end with a brief discussion of approaches to distinguishing these underlying configurations empirically.