TY - JOUR

T1 - Distributional assumptions and observed conservatism in the theory of signal detectability

AU - Maloney, Laurence T.

AU - Thomas, Ewart A C

N1 - Funding Information:
Reprint requests should be sent to Laurence T. Maloney, who is now at the Department Psychology, 8th Floor, New York University, 6 Washington Place, New York, New York 10003. This work was supported in part by an associateship awarded to the first author by the National Research Council of the National Academy of Sciences administered through the NASA Ames Research Center, Life Sciences Division, at Moffett Field, Mountain View, CA and in part by a grant to the first author from the National Eye Institute, EY08266. We are grateful for comments provided by Jean-Claude Falmagne, David H. Krantz, Donald R. J. Laming, Michael S. Landy, David E. Meyer, A. A. J. Marley, James T. Townsend, and an anonymous reviewer whose comments much improved the presentation.

PY - 1991/12

Y1 - 1991/12

N2 - The theory of signal detectability typically fits data from Yes-No detection experiments by assuming a particular form for the noise and signal plus noise distributions of the Observer. Previous work suggests that estimates of the Observer's sensitivity are little affected by small discrepancies between the assumed distributions (usually Gaussian) and the Observer's true underlying distributions. Possibly for this reason, estimates of the Observer's choice of criterion or likelihood ratio suggesting suboptimal performance have also been taken at face value. It is, for example, commonly accepted that human Observers are conservative: They are said to choose criteria corresponding to likelihood ratios that are closer to 1 than the ratios produced by optimal criteria. We demonstrate that estimates of likelihood ratio can be markedly biased when the distributions assumed in estimation are not the Observer's true distributions. We derive necessary and sufficient conditions for an optimal Observer to appear conservative when fitted by distributions different from those governing his choices. These results raise a fundamental question: What information about the Observer's underlying noise and signal plus noise distributions does the Observer's performance in a Yes-No detection task provide? We demonstrate that a small number of isosensitivity (ROC) curves completely determines the Observer's underlying noise and signal plus noise distributions for many familiar forms of the theory of signal detectability. These results open up the possibility of a semiparametric theory of signal detectability.

AB - The theory of signal detectability typically fits data from Yes-No detection experiments by assuming a particular form for the noise and signal plus noise distributions of the Observer. Previous work suggests that estimates of the Observer's sensitivity are little affected by small discrepancies between the assumed distributions (usually Gaussian) and the Observer's true underlying distributions. Possibly for this reason, estimates of the Observer's choice of criterion or likelihood ratio suggesting suboptimal performance have also been taken at face value. It is, for example, commonly accepted that human Observers are conservative: They are said to choose criteria corresponding to likelihood ratios that are closer to 1 than the ratios produced by optimal criteria. We demonstrate that estimates of likelihood ratio can be markedly biased when the distributions assumed in estimation are not the Observer's true distributions. We derive necessary and sufficient conditions for an optimal Observer to appear conservative when fitted by distributions different from those governing his choices. These results raise a fundamental question: What information about the Observer's underlying noise and signal plus noise distributions does the Observer's performance in a Yes-No detection task provide? We demonstrate that a small number of isosensitivity (ROC) curves completely determines the Observer's underlying noise and signal plus noise distributions for many familiar forms of the theory of signal detectability. These results open up the possibility of a semiparametric theory of signal detectability.

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U2 - 10.1016/0022-2496(91)90043-S

DO - 10.1016/0022-2496(91)90043-S

M3 - Article

AN - SCOPUS:38149144377

SN - 0022-2496

VL - 35

SP - 443

EP - 470

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

IS - 4

ER -