Beyond Binary Responses

In a single session of a yes-no experiment we can collect data that can be interpreted as multiple ( F , H ) pairs. An empirical receiver operating characteristic (ROC) curve is obtained by asking observers to provide a graded rather than a binary response, rating their experience on an ordered scale. The data are interpreted as if the observer maintained several response criteria simultaneously. If the empirical ROC has a unit slope on z -coordinates, the sensitivity measure will be the same at all criteria. If the slope of the z -ROC does not equal 1, apparent sensitivity changes along the decision axis. The slope can be interpreted as the ratio of the standard deviations of the underlying normal distributions. Sensitivity can be measured in units of either standard deviation, or some sort of average. Alternative ways to get multiple points on an empirical ROC include conducting separate sessions with different a priori probabilities, payoffs and penalties for the various outcomes, or instructions.

Arithmetic · Binary number · Critical Race Theory in Education · Interdisciplinary Cultural and Social Studies · Latin American and Latino Studies · Mathematics