Clarifications for calculating area under the curve for discounting data: A primer and technical report

Abstract

Discounting is a pervasive phenomenon in human decision making and has been extensively studied across disciplines. This article focuses on area under the curve (AUC) as a popular measure of discounting. We provide a comprehensive review of AUC in relation to discounting, focusing on its atheoretical underpinnings and methods to calculate the measure. Additionally, we delve into the limitations of traditional AUC measures and limitations of more recent modifications of AUC (i.e., ordinal and logarithmic AUC). First, authors using AUC do not routinely report whether and how they impute an indifference point at the y-intercept, which is critically important when using the ordinal or logarithmic versions. Additionally, the ordinal version of AUC requires removing the x-axis information (e.g., delay, odds against, social distance, etc.) and replacing them with ordinal values. The logarithmic version of AUC often introduces nonintuitive values on the x-axis that lead to a high likelihood of miscalculations. We propose that authors always impute an indifference point at the y-intercept—when such data were not collected—and propose a novel method to shift indifference points that leads to a more intuitive logarithmic AUC calculation. An R package and Excel workbook to help calculate AUC are also provided and discussed.