Intrinsic uncertainty explains second responses.

In the simplest form of signal-detection theory (SDT), all stimuli give rise to equal-variance Gaussian probability density functions (PDFs) of sensation, with means proportional to stimulus intensity. As this simple SDT cannot accurately describe psychometric functions for two-alternative forced-choice (2AFC) detection experiments, it is commonly modified in one of two ways: with a non-linear transducer or intrinsic uncertainty. Most results can adequately be explained by either modification, but Swets et al.'s (1961) two-response 4AFC (2R4AFC) detection experiment is an exception. Simple SDT cannot predict the relationship between first- and second-response accuracies and non-linear transduction does not help. A previously unacknowledged facet of intrinsic uncertainty is that the same uncertainty required to fit 2AFC psychometric functions also produces an excellent fit to Swets et al.'s 2R4AFC results, without requiring any additional assumptions. This result is derived within the context of a primer on SDT.