Psychometric functions for the power-function transducer with nonzero pedestal.

<p>The psychometric function for was generated using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074815#pone.0074815.e453" target="_blank">Equation (71</a>); the others were generated using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074815#pone.0074815.e430" target="_blank">Equation (69</a>). In both cases, we assumed Gaussian internal noise (i.e. <i>F</i> is the cumulative Gaussian). All the psychometric functions go through the point , by definition of the threshold (the abscissa is in threshold units, i.e. ). Each panel shows psychometric functions for a particular Weber fraction. Each curve within a panel shows the psychometric function for a particular transducer exponent, <i>b</i>. The orange curve () is the psychometric function plotted in green in the second-to-top row of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074815#pone-0074815-g010" target="_blank">Figure 10</a>. The blue curve () is the psychometric function plotted in green in the second-to-top row of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074815#pone-0074815-g011" target="_blank">Figure 11</a>. The black line shows the limit as . As proved in Theorem 4A, this limiting case is identical to the psychometric function for a log transducer. This is the psychometric function plotted in green in the second-to-top row of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074815#pone-0074815-g012" target="_blank">Figure 12</a>. This figure illustrates two effects. Within each panel, we see how the psychometric function for the power-function transducer converges towards that for a log transducer as the exponent decreases (Theorem 4). Across panels (right-to-left), we see a demonstration of the effect proved in Theorem 3, whereby, with a nonzero pedestal, all psychometric functions converge towards that for a linear transducer as the discrimination threshold decreases (in this case, since we are plotting psychometric functions for Gaussian noise, the functions converge towards the pure noise CDF of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074815#pone-0074815-g004" target="_blank">Figure 4B</a> as the Weber fraction decreases).