Models for the duo-trio and triangular methods

Duo-trio and triangular method models by Ura (1960, Japanese Union of Scientists and Engineers 7, 107-119) and David and Trivedi (unpublished Technical Report #55, Department of Statistics, Virginia Polytechnic Institute, 1962) for examining perceptual processes have proven to be very useful, but are limited to univariate phenomena. Recent Monte Carlo studies by Ennis and Mullen (1985, Chemical Senses 10, 605-608; 1986, Journal of Mathematical Psychology 30, 206-219), on the probabilities of correct decisions for multivariate responses, showed how they depend on discriminal distance, variance-covariance structure, and orientation in n-space. Mathematical models for the triangular and duo-trio method in the bivariate case were developed by Mullen and Ennis (1987, Psychometrika 52, 235-249). Formulation of the n-dimensional triangular method model was accomplished and problems in numerical integration were resolved by Kapenga et al. (1987, in Numerical Integration, P. Keast and G. Fairweather (eds), 321-328; Dordrecht: Reidel). The n-dimensional duo-trio method model is given in this paper and previous work on the triangular method is reviewed briefly.