Volume 125, May 2025, 102919Author links open overlay panelHighlights•

A novel model was derived describing uncertainty as the total entropy of the psychometric function and stimuli.

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The model is generalized and can be applied to different types of decisions.

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This model was applied to test the question of whether paying attention to a stimulus changes its appearance.

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Attentional cues affected uncertainty differently than did explicit bias instructions, even while producing indistinguishable reports.

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Although different decision mechanisms produce different uncertainty distributions, they may be based on the same underlying parameters.

Abstract

Studying metacognition, the introspection of one's own decisions, can provide insights into the mechanisms underlying the decisions. Here we show that observers’ uncertainty about their decisions incorporates both the entropy of the stimuli and the entropy of their response probabilities across the psychometric function. Describing 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 as 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

Metacognition

Confidence

Uncertainty

Attention

Perception

Vision

Appearance

Data availabilityThe data, collected between Nov. 2012 and Jan. 2013, and the stimuli and analysis codes, written exclusively by the author, are available at http://osf.io/f3stc.

© 2025 The Author. Published by Elsevier Inc.