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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

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