Berkson’s Paradox
Why do the handsome ones seem to be jerks? Why do hospital patients show diseases correlating that don’t correlate in the street? Berkson’s paradox: selection manufactures correlation. This simulator scatters N points with two independent traits (a slider sets the true correlation, zero by default) and applies a selection rule — keep anyone whose traits sum above a threshold, or the top k by total. Inside the selected group the correlation turns sharply negative: among those who cleared the bar, being high on one trait means the other didn’t need to be. Both correlations are displayed with their regression lines, a toggle dims the rejected points to show the world as the selector sees it, and presets tell the classic stories — the dating filter, hospital comorbidity, and talented-versus-attractive actors.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Conditioning on a collider creates dependence: if selection depends on x + y, then within the selected set knowing x is high tells you y could afford to be low — a negative correlation born entirely from the cut.
- Berkson described it in 1946 for hospital studies: two diseases that are independent in the population correlate among inpatients, because having either raises the chance of admission.
- The dating-pool version: if people must be attractive or kind enough (in sum) to date at all, then within the pool attractiveness predicts less kindness — even when the traits are independent in humanity at large.
- The cure is knowing your denominator: every dataset gathered through a filter — admissions, hiring, publication — carries built-in correlations that say more about the filter than about the world.
- Runs 100% in your browser — simulations are computed locally on your device.
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