Abstract
An optimal decision strategy for deciding whether two things are the same or different is to adopt a likelihood-ratio criterion. The parametric equations for the receiver operating characteristic (ROC) based on the likelihood-ratio strategy when observations are independent are complicated; they require the numerical evaluation of a double integral. An approximation to the parametric equations for the likelihood-ratio strategy was developed. This approximation takes the form of a pair of equations that describe ROCs virtually indistinguishable from those of the full model.
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Dai, H., Versfeld, N., &Green, D. (1996). The optimum decision rules in thesame-different paradigm.Perception & Psychophysics,58, 1–9.
Green, D. M., &Birdsall, T. G. (1978). Detection and recognition.Psychological Review,85, 192–206.
Green, D. M., &Swets, J. A. (1966).Signal detection theory and psychophysics. New York: Wiley.
Hautus, M. J., Irwin, R. J., &Sutherland, S. (1994). Asymmetry in thesame-different ROC and the relativity of judgments about sound amplitude.Quarterly Journal of Experimental Psychology,47A, 1035–1045.
Johnson, K. O. (1980). Sensory discrimination: Decision process.Journal of Neurophysiology,43, 1771–1792.
Laming, D. (1986).Sensory analysis. London: Academic Press.
Macmillan, N. A., &Creelman, C. D. (1991).Detection theory: A user’s guide. Cambridge: Cambridge University Press.
Macmillan, N. A., Kaplan, H. L., &Creelman, C. D. (1977). The psychophysics of categorical perception.Psychological Review,84, 452–471.
Nolte, L. W., &Jaarsma, D. (1967). More on the detection of one of Morthogonal signals.Journal of the Acoustical Society of America,41, 497–505.
Noreen, D. L. (1981). Optimal decision rules for some common psychophysical paradigms. In S. Grossberg (Ed.),Proceedings of the Symposium in Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics (Vol. 13, pp. 237–279). Providence: RI: American Mathematical Society.
Sorkin, R. D. (1962). Extension of the theory of signal detectability to matching procedures in psychoacoustics.Journal of the Acoustical Society of America,34, 1745–1751.
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Irwin, R.J., Hautus, M.J. Likelihood-ratio decision strategy for independent observations in thesame-different task: An approximation to the detection-theoretic model. Perception & Psychophysics 59, 313–316 (1997). https://doi.org/10.3758/BF03211898
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DOI: https://doi.org/10.3758/BF03211898