The amplitude of white noise is Gaussian-distributed. That randomness may limit the detectability of an intensity change from interval to interval. Green (1960) and deBoer (1966) assumed that the detected change was that of average power, which for a single listening interval T, and noise bandwidth W, is the integral of the squared amplitude divided by T, approximated by (1/2WT) times the sum of 2WT samples of the square of the amplitude. Noises of differing intensities result in Gaussian-distributed average-power distributions having differing means and variances. The Signal Detection Theory "dprime" equals the difference between two means, divided by the square root of half of the sum of the two variances. dprime, and the increment power divided by the noise power, called S/N, are both unitless positive real numbers, setting a maximum to dprime. The difference limen (DL) is a simple logarithmic equation in S/N. Psychophysical studies show that the empirical DLs exceed the predicted DLs. To eliminate that discrepancy, deBoer (1966) and Raab & Goldberg (1975) added a Gaussian-distributed, zero-mean “physiological noise” to the Gaussian-distributed average powers. But their corrected dprime does not produce a real-valued and positive S/N. Green & Swets (1966/1988) and Shofner, Yost, & Sheft (1993) proposed an alternative incorporation of “physiological noise”. But their dprime's can only be derived with fewer than 2WT samples of noise amplitude. These latent flaws may explain the poor fit of all these authors' DL equations to their empirical DLs. |