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Testing the difference between two Kolmogorov--Smirnov values in the context of receiver operating characteristic curves

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  • Wojtek J. Krzanowski
  • David J. Hand

Abstract

The maximum vertical distance between a receiver operating characteristic (ROC) curve and its chance diagonal is a common measure of effectiveness of the classifier that gives rise to this curve. This measure is known to be equivalent to a two-sample Kolmogorov--Smirnov statistic; so the absolute difference D between two such statistics is often used informally as a measure of difference between the corresponding classifiers. A significance test of D is of great practical interest, but the available Kolmogorov--Smirnov distribution theory precludes easy analytical construction of such a significance test. We, therefore, propose a Monte Carlo procedure for conducting the test, using the binormal model for the underlying ROC curves. We provide Splus/R routines for the computation, tabulate the results for a number of illustrative cases, apply the methods to some practical examples and discuss some implications.

Suggested Citation

  • Wojtek J. Krzanowski & David J. Hand, 2011. "Testing the difference between two Kolmogorov--Smirnov values in the context of receiver operating characteristic curves," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 437-450, October.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:3:p:437-450
    DOI: 10.1080/02664760903456400
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    Cited by:

    1. Kenneth P. Brevoort & Robert B. Avery & Glenn B. Canner, 2013. "Credit Where None Is Due? Authorized-User Account Status and Piggybacking Credit," Journal of Consumer Affairs, Wiley Blackwell, vol. 47(3), pages 518-547, November.
    2. Alba M. Franco-Pereira & Christos T. Nakas & M. Carmen Pardo, 2020. "Biomarker assessment in ROC curve analysis using the length of the curve as an index of diagnostic accuracy: the binormal model framework," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 625-647, December.

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