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A Note on ROC Analysis and Non-Parametric Estimate of Sensitivity

Published online by Cambridge University Press:  01 January 2025

Jun Zhang  and
Shane T. Mueller
Jun Zhang*
Affiliation:
University of Michigan at Ann Arbor
Shane T. Mueller
Affiliation:
University of Michigan at Ann Arbor
*
Requests for reprints should be sent to Jun Zhang, Department of Psychology, University of Michigan, 525 East University, Ann Arbor, MI 48109, USA. E-mail: [email protected]
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Abstract

In the signal detection paradigm, the non-parametric index of sensitivity A′, as first introduced by Pollack and Norman (1964), is a popular alternative to the more traditional d′ measure of sensitivity. Smith (1995) clarified a confusion about the interpretation of A′ in relation to the area beneath proper receiver operating characteristic (ROC) curves, and provided a formula (which he called A′′) for this commonly held interpretation. However, he made an error in his calculations. Here, we rectify this error by providing the correct formula (which we call A) and compare the discrepancy that would have resulted. The corresponding measure for bias b is also provided. Since all such calculations apply to “proper” ROC curves with non-decreasing slopes, we also prove, as a separate result, the slope-monotonicity of ROC curves generated by likelihood-ratio criterion.

Keywords

signal detection theoryA′non-parametric estimate of sensitivitylikelihood-ratio
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 1 , March 2005 , pp. 203 - 212
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

†

Now at Department of Psychology, 1101 East 10th Street, Indiana University, Bloomington, IN 47405, USA

References

Ashby, F.G., Townsend, J.T. (1986). Varieties of perceptual independence. Psychological Review, 93, 154–179.CrossRefGoogle ScholarPubMed
Balakrishnan, J.D. (1998). Some more sensitive measures of sensitivity and response bias. Psychological Methods, 3, 68–90.CrossRefGoogle Scholar
Balakrishnan, J.D. (1999). Decision processes in discrimination: fundamental misrepresentations of signal detection theory. Journal of Experimental Psychology: Human Perception and Performance, 25, 1189–1206.Google ScholarPubMed
Donaldson, W., Good, C. (1996). A’r: An estimate of area under isosensitivity curves. Behavioral Methods, Instruments, and Computers, 28, 590–597.CrossRefGoogle Scholar
Green, D.M., Swets, J.A. (1964). Signal Detection Theory and Psychophysics. New York: John Wiley & Sons.Google Scholar
Macmillan, N.A., Creelman, C.D. (1996). Triangles in ROC space: History and theory of “non-parametric” measures of sensitivity and response bias. Psychonomic Bulletin and Review, 3, 164–170.CrossRefGoogle Scholar
Newsome, W.T., Britten, K.H., Movshon, J.A., Shadlen, M. (1989). Single neurons and the perception of visual motion. In Lam, D.M-K., Gilbert, C.D. (Eds.), Proceedings of the Retina Research Foundation Symposia, Vol. 2, Neural Mechanisms of Visual Perception (pp. 171–198). Woodlands, TX: Portfolio Publishing.Google Scholar
Peterson, W.W., Birdsall, T.G., Fox, W.C. (1954). The theory of signal detectability. Transactions of the IRE Professional Group on Information Theory, PGIT-4, 171–212.CrossRefGoogle Scholar
Pollack, I., Hsieh, R. (1969). Sampling variability of the area under ROC curve and ′-e. Psychological Bulletin, 1, 161–173.CrossRefGoogle Scholar
Pollack, L., Norman, D.A. (1964). Non-parametric analysis of recognition experiments. Psychonomic Science, 1, 125–126.CrossRefGoogle Scholar
Smith, W.D. (1995). Clarification of sensitivity measure A′. Journal of Mathematical Psychology, 39, 82–89.CrossRefGoogle Scholar
Swets, J.A., Tanner, W.P., Birdsall, T.G. (1964). Decision process in perception. Psychological Review, 68, 301–340.CrossRefGoogle Scholar
Tanner, W.P. Jr., Swets, J.A. (1954). A decision-making theory of visual detection. Psychological Review, 61, 401–409.CrossRefGoogle ScholarPubMed
Zhang, J., Riehle, A., Requin, J. (1997). Locus of a neural process in stimulus-response association tasks. Journal of Mathematical Psychology, 41, 219–236.CrossRefGoogle ScholarPubMed