Studying metacognition, the introspection of one's own decisions, can provide insights into the mechanisms underlying the decision. Here we show that observers' uncertainty about their decisions incorporate both the entropy of the stimuli and the entropy of their response probability across the psychometric function. Being able to describe uncertainty data with a functional form permits the measurement of internal parameters not measurable from the decision responses alone. To test and demonstrate the utility of this novel model, we measured uncertainty in 11 participants as they judged the relative contrast appearance of two stimuli in several experiments employing implicit bias or attentional cues. The entropy model enabled an otherwise intractable quantitative analysis of participants' uncertainty, which in one case distinguished two comparative judgments that produced nearly identical psychometric functions. In contrast, comparative and equality judgments with different behavioral reports, yielded uncertainty reports that were not significantly different. The entropy model was able to successfully account for uncertainty in these two different types of decisions that resulted in differently shaped psychometric functions, and the entropy contribution from the stimuli, which were identical across experiments, was consistent. An observer's uncertainty could therefore be measured the total entropy of the inputs and outputs of the stimulus-response system, i.e. the entropy of the stimuli plus the entropy of the observer's responses.
Keywords: appearance; attention; confidence; metacognition; perception; uncertainty; vision.