The average slope of the cochlear nonlinearity versus the width of psychometric functions (see text). Some of this illustration resembles Figure 3, with one major change: the two-line-segment model of Schairer et al.  for the cochlear nonlinearity is replaced by a smoothly-changing cochlear nonlinearity modified from the animal literature (chinchilla cb24; ). Otherwise, as in Figure 3, the (assumed constant) width of the output distribution determines the width of the input distribution. In a step beyond, however, the input distribution is also presumed to be integrated to yield the psychometric function for probe-tone detection, which must run from a minimum of 0.5 to a maximum of 1 in Experiments 1 and 2. μ is the probe-tone detection threshold, which is the mean value of the input distribution. The solid dot ● indicates the centroid of the psychometric function, found for μ , and the open square □ is the corresponding locus on the cochlear nonlinearity. The width of the psychometric function is defined as 2nσ , where n∈+Ι , and its corresponding points on the cochlear nonlinearity are marked by the open circles ○. Through those circles passes the dashed slanted line, whose slope is the average of the slopes between the two ○’s, and which approximates the slope of the cochlear nonlinearity at □. These slopes are better approximations than may seem from this illustration, as the input distributions (and corresponding psychometric function) shown here are (as in Figure 3) at least twice as wide as suggested from the empirical psychometric functions of Experiments 1 and 2. Note that the psychometric function does not have units of dB, but rather “percentage correct”, and as such should be considered as a projection upon the plane of the graph.