Clarifications for calculating area under the curve for discounting data: A primer and technical report
Use Friedel’s free code and always add the y-intercept so your AUC numbers are right.
01Research in Context
What this study did
Friedel et al. (2025) wrote a how-to guide for AUC math. AUC means area under the curve. It shows how steeply someone discounts future rewards.
The team spotted three steps many labs skip. They built free R and Excel tools that plug the holes. No new data were collected.
What they found
The authors show you must add a y-intercept indifference point before you integrate. Skip it and your AUC shrinks.
Their code does this auto-fix and handles log-scaled x-axes.
How this fits with other research
Rzeszutek et al. (2023) used AUC math to study pandemic choices. They followed the old steps. Friedel’s guide tightens their numbers.
Raineri et al. (2024) compared Chile and China with hyperboloid AUC. Friedel’s tools now give cleaner cross-culture areas.
DeHart et al. (2019) wrote a primer on mixed-effects for single-case data. Friedel does the same job for discounting curves.
Barnard-Brak et al. (2020) gave Bayesian N-of-1 code. Friedel gives AUC code. Both papers hand practitioners ready-to-run scripts.
Why it matters
If you run delay or probability discounting tasks, use the new tools. Paste your data, click run, and get the right AUC. You will stop mis-rating impulsivity in clients with ADHD or substance use.
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02At a glance
03Original 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.
Journal of the Experimental Analysis of Behavior, 2025 · doi:10.1002/jeab.70041