Reply to 'The unique criterion constraint: a false alarm?'

707 TO THE EDITOR—In a recent paper in Nature Neuroscience, Gorea and Sagi1 proposed a novel method for estimation of the separate signal and noise components of the contrast transducer in humans. Their experimental task requires detection, simultaneously, in two locations of contrast increments differing by either increment value (see their Fig. 3b) or baseline contrast (their Fig. 4a). In this mixed task, observers adopt a common false alarm rate (FA) for both locations2 to provide separate estimates of the transducer exponents for the signal and the noise, which took the form of a compressive signal nonlinearity and an almost constant noise. In the Gorea and Sagi task, however, the only independent quantities are FA and the discriminability (d′) derived through signal detection theory. These quantities both depend on the signal-to-noise ratio governing performance rather than on the signal transducer alone. To overcome these basic limitations of psychophysics, Gorea and Sagi1 introduce a “unique criterion constraint” for all attended stimuli that is critical for their subsequent analysis of mixed-stimulus situations. They show that the assumption of a single criterion is appropriate for same-baseline conditions and then generalize this assumption to mixed-pedestal situations where the properties of the noise sources are at issue. Formally, the criterion c is linked to the false alarm rate through the expression