Fig. 4.

Example fits for a human test. A: example stimulus track, including confidence probability judgments, is shown for first 20 trials. Upward-pointing gray triangles and downward-pointing black triangles represent rightward and leftward trials, respectively. B: following 20 binary forced-choice trials, a conventional psychometric function (black curve), $\widehat{\Psi }\left(x\right)=\varphi \left(x;\widehat{\mu }=0.05,\widehat{\sigma }=0.95\right)$, was fit to the binary forced-choice data points shown. C: given the same 20 trials with confidence probability judgments, a psychometric function (black curve), $\widehat{\Psi }\left(x\right)=\varphi \left(x;\widehat{\mu }=0.19,\widehat{\sigma }=0.91\right)$, and a confidence function (gray curve), $\widehat{\chi }\left(x\right)=\varphi \left(x;\widehat{\mu }=0.19,\widehat{k}\widehat{\sigma }=1.43\right)$, were simultaneously fit to the confidence data. All example data are from one of the human data sets (Fig. 5, D, H, and L) presented herein. For comparison, the fitted psychometric function determined after 100 binary forced-choice trials using conventional methods, $\widehat{\Psi }\left(x\right)=\varphi \left(x;\widehat{\mu }=0.33,\widehat{\sigma }=0.59\right)$, is also shown via dashed lines in B and C. Half-scale (50 to 100%) probability judgments provided by subjects have been converted to full-scale (0 to 100%) judgments as described in methods.