Distribution curves for amplitude (envelope), drawn for noise and for noise plus signal, provide the basis for determining the proportion of area (probabilities) lying above various “criterion” levels. Probability pairs P (y∣n) and P (y∣sn) for various criterion levels furnish the coordinates of points generating ROC curves, which, because of the skewness of the distributions, show a slight curvature when plotted on normal‐normal paper. This curvature (concave downward) provides a better fit to detection data obtained from rating‐scale experiments than do the straight lines obtained from normal curves. The ROC curves belong to a family derived through the theory of signal detectability for the ideal observer in the case where signal phase is unspecified. The fact that the distribution for noise‐plus‐signal amplitudes has, in general, a larger variance than that for noise alone explains why many experiments find the ratio of σsn to σn to be greater than unity. A detection measure d, derived from the two distribution curves, when plotted against signal amplitude, is a straight line over most of its course but bends in to the origin for weak signals. Its failure to touch the positive abscissa supports the TSD argument against the threshold hypothesis. A second curve, derived from this one, provides a convenient way of determining the signal required to yield a particular value of ds, when the signal that yields some other value of ds is known. Finally, the concept of “effective bandwidth” is developed, and provides a single parameter for use in fitting detection data. Data give some support for the notion that the auditory system adjusts its bandwidth in accordance with the duration of the signal.