Detection-theoretic analysis of same-different judgments for the amplitude discrimination of acoustic sinusoids

Three methods were applied to determine which decision model best accounted for same-different judgments about the amplitude of acoustic sinusoids. The methods were (1) analysis of the shape of the receiver operating characteristic; (2) analysis of an observer's decision space; and (3) a correlation method based on the conditional-on-single-stimulus procedure. In one experiment, observers rated their confidence that a pair of 1-kHz sinusoids was drawn from the same or from different sets. The two sets had identical Gaussian distributions of decibel amplitudes, but their mean amplitudes differed by 3 dB. The differencing model, in which observers base their decision on the absolute difference between the two observations, accounted for the data better than the independent-observation model, in which observers compute independent likelihood ratios for each observation. A second experiment added to every trial an interval that contained a 1-kHz sinusoid whose amplitude equaled the grand mean of both stimulus sets. Despite this additional information, which is needed to adopt the independent-observation model, the differencing model again better accounted for the data.