Berkson's paradox - Wikipedia

Abstraction: Spurious negative correlation arising from conditioning on a collider variable

Key points:

• Berkson's paradox (also collider bias or endogenous selection bias) occurs when sampling from a filtered subset creates a false negative correlation between two otherwise independent traits
• Classic example: hospital patients without diabetes are more likely to have cholecystitis than the general population because their hospitalization implies some other cause
• Dating pool example (Jordan Ellenberg): within the pool of people meeting a minimum niceness+handsomeness threshold, nicer individuals appear less handsome, even if traits are uncorrelated in the full population
• Formally, two independent events A and B become conditionally dependent given that at least one occurs (P(A|B,A∪B) < P(A|A∪B))
• The effect is related to "explaining away" in Bayesian networks and conditioning on a collider in graphical causal models

Connections: Joseph Berkson · Jordan Ellenberg · Selection Bias · Collider Bias · Conditional Probability · Bayesian Networks

Source: https://en.wikipedia.org/wiki/Berkson's_paradox