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

Chao Zhou

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arXiv · 2605.11017

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

Chao Zhou

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Abstract

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.

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Chao Zhou. 2026-07-23. Simpson's Paradox in Behavioral Curves: How Aggregation Distorts Parametric Models of User Dynamics. https://arxiv.org/abs/2605.11017

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