The N-Alternative Optional Choice Experiment

When testing visual function in clinical settings, one encounters test-takers who have difficulty following a forced-choice instruction when stimulus intensity is low. “I didn’t see anything, why do I have to guess?” An optional-choice paradigm makes it easier for these test-takers to provide data. Here we describe a theory of signal detection for N-alternative optional-choice (N-AOC) psychophysical tasks. The theory generalizes two well-known paradigms into a single framework: the theory for yes-no tasks is a degenerate case in which N=1, and the theory for N-alternative forced choice tasks (N-AFC) is a degenerate case in which the decision criterion is liberal. A different generalization, that can be applied either to yes-no or to N-AFC (and that we were reminded of by Jeffrey Mulligan), is to collect the observer’s confidence judgment on each trial. Confidence judgments are easily incorporated into N-AOC as well.