Abstract
According to a well-known theorem in psychophysics (Green & Swets, 1966), the area under the receiver operating characteristic (ROC) for the yes—no paradigm equals the proportion of correct responses of an unbiased observer in the two-interval, two-alternative, forced choice paradigm (2I2AFC). Here, we demonstrate a similar relationship between the ROC area in the two-interval same—different (AX or 2IAX) paradigm, and the proportion correct in the four-interval same—different (4IAX, also known as dual-pair comparison) paradigm. The theorem demonstrated here is general, in the sense that it does not require that the sensory observations have a specific distribution (e.g., Gaussian), or that they be statistically independent.
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This work was supported in part by NIH Grant R01 DC 05216 to C.M.
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Micheyl, C., Dai, H. A general area theorem for the same—different paradigm. Perception & Psychophysics 70, 761–764 (2008). https://doi.org/10.3758/PP.70.5.761
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DOI: https://doi.org/10.3758/PP.70.5.761