AIDAID202 · Lectures 7–8

Lecture 7 · Probability review

Dependence can disappear when we condition

A variable can make two other variables look related even when they are independent after conditioning on it.

Predict first: Taxi drivers wearing coats have more accidents. Does that imply coats increase accident risk?

Expected outcomes in 10,000 driving periods

P(accident | coat)—
P(accident | no coat)—

Condition on weather

Reveal the point

If coat use and accidents are both driven by rain, they can be statistically dependent marginally even when P(A,C | Rain)=P(A|Rain)P(C|Rain) and the same holds when it is dry.

Conditioning on the relevant variable removes the information that coat-wearing was indirectly providing about weather.