The estimation of a non‐parametric measure of signal discriminability is discussed and its behaviour investigated under the following conditions: (a) when the ‘trace’ distributions for the two signals being compared differ only by a shift parameter, Λ (b) when the probability density function of the trace is a monotone likelihood ratio; and (c) when the subject bases his response on a likelihood‐ratio rule, with a constant criterion. In this case the measure of discriminability is an increasing function of the shift, A. This monotonicity also holds for the two‐response experiment under rather more general conditions. Data from such an experiment are used as