# Simpson's Paradox in Behavioral Curves: How Aggregation Distorts Parametric Models of User Dynamics

arXiv: https://arxiv.org/abs/2605.11017 · HTML: https://mlsanity.com/paper/2605.11017/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 30 references that are in the map.
- First posted on arXiv 10 May 2026.

## Builds on (most cited first, 2 of 2)

- [Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits](https://mlsanity.com/paper/1402.0555/) (2014)
- [Using Simpson's Paradox to Discover Interesting Patterns in Behavioral Data](https://mlsanity.com/paper/1805.03094/) (2018)

## Abstract (arXiv)

Behavioral curve modeling -- fitting parametric functions to engagement-versus-exposure data -- is standard practice in recommendation, advertising, and clinical dosing. We show that aggregation introduces a systematic distortion: Simpson's paradox in behavioral curves. On Goodreads (3.3M users, 9 genres), individual users peak at n* approximately 11 exposures while the aggregate peaks at n* approximately 34 -- a 3x gap driven by survival bias. Amazon Electronics (18M reviews) shows a 5.3x distortion. MovieLens-25M (D approximately 1) serves as a negative control, confirming that survival bias -- not aggregation per se -- is the operative mechanism. The distortion is robust to category granularity, engagement operationalization, and classifier calibration. We develop Synthetic Null Calibration to address a 32% false positive rate in per-user classification. Our findings apply wherever individual behavioral parameters are estimated from aggregate curves under differential attrition.