The relative psychometric function: a general analysis framework for relating psychological processes

Psychophysics seeks to quantitatively characterize relationships between objective properties of the world and subjective properties of perception. However, traditional approaches investigate psychophysical dependencies of perception on stimulus properties on a case by case basis rather than seeking to identify quantitative relationships among these psychological processes themselves. This latter goal is particularly important when the processes in question likely depend on each other in some way, such as is the case for subjective experience and task performance: typically, stronger physical stimuli lead to better performance and stronger subjective experiences of clarity, vividness, or confidence. But is the relationship between performance and subjective experience fixed, or can it vary, e.g. by task or attentional demands? Such questions are key for better understanding psychological processes in general, and subjective experience in particular. Here, we develop and showcase a new psychophysical method designed to answer such questions: relative psychometric function (RPF) analysis, which characterizes the nonlinear psychometric relationships between psychological processes and how these relationships change under different circumstances (e.g. experimental manipulations). We demonstrate the advantages of RPF analysis using a sample dataset in which human subjects discriminated random dot kinematogram stimuli which varied in dot motion coherence and overall dot density (dots per visual degree), and rated confidence. RPF analysis revealed systematic changes in the relationship between performance and two subjective measures (confidence and metacognitive sensitivity) due to dot density and task design choices. While these empirical results are intriguing in their own right, they also show how RPF analysis can reveal changes in quantitative relationships between any two psychological measures: performance, vividness, clarity, reaction time, confidence, and more. To encourage the scientific community to use RPF analysis on their data, we also present our open-source RPF toolbox.