Diagonal d' does not (always) diagnose failure of separability: An addendum to.

Kingston, Diehl, Kirk, and Castleman (Journal of Phonetics, 2008) 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.