Alternative performance index to analyze receiver operating characteristic data under the exponential assumption

1 April 2006 Alternative performance index to analyze receiver operating characteristic data under the exponential assumption

Francisco J. Sanchez-Marin, Jose A. Padilla-Medina

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Journal of Electronic Imaging, Vol. 15, Issue 2, 023009 (April 2006). https://doi.org/10.1117/1.2195462

Abstract

Thirty human observers are tested in a visual detection task under the rating receiver operating characteristic (ROC) paradigm. Since most of the observers were not able to use the rating categories as instructed, their data are excluded from the analysis. From the 30 observers, the four best and most experienced are selected to do long experiments (with 1000 presentations). However, the assumption of Gaussians with equal variance of classical ROC theory is not satisfied by the new data. Nevertheless, assuming Gaussian underlying distributions with unequal variances, the three well-known indices of performance d_m, d_e, and d_x are calculated in terms of the geometry of the linear fits in normal deviated coordinates. The areas under the ROC curves are also calculated. We found that the power-law ROC, which assumes underlying exponential distributions, fit well our data. Under the exponential-exponential assumption, we derive a new performance (detectability) index that is easily calculated from experimental data and that depends on a single parameter. The obtained values of the proposed index are in agreement with the corresponding values of the d_m, d_e, and d_x indices, but with the new index it is much easier to discriminate between observers with similar performance with considerably lower uncertainty.

©(2006) Society of Photo-Optical Instrumentation Engineers (SPIE)

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Francisco J. Sanchez-Marin and Jose A. Padilla-Medina "Alternative performance index to analyze receiver operating characteristic data under the exponential assumption," Journal of Electronic Imaging 15(2), 023009 (1 April 2006). https://doi.org/10.1117/1.2195462

Published: 1 April 2006

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