= Average treatment effect
{title2=ATE}
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The <average treatment effect> in a target population is $\mathbb E[Y(1)-Y(0)]$, the average additive contrast between two <potential outcomes>. It does not require every individual effect to be the same. If half the population has effect two and half effect minus one, the <average treatment effect> is $1/2$. Under <consistency in causal inference>, <conditional exchangeability> given pretreatment covariates $X$, and <positivity>, it is identified by $\mathbb E_X[\mathbb E(Y\mid A=1,X)-\mathbb E(Y\mid A=0,X)]$. The outer average uses the specified target population, not whichever <group> happens to be observed most often.
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