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The treatment effect for individual <math>i</math> is given by <math>y_{1}(i)-y_{0}(i)=\beta(i)</math>. In the general case, there is no reason to expect this effect to be constant across individuals. The average treatment effect is given by  

The treatment effect for individual <math>i</math> is given by <math>y_{1}(i)-y_{0}(i)=\beta(i)</math>. In the general case, there is no reason to expect this effect to be constant across individuals. The average treatment effect is given by  

个体 <math> i </math> 的处理效应定义为 <math> y_{1}(i)-y_{0}(i) = \beta (i) </math> 。在一般情况下，这种处理效果在个体之间是不一样的。平均处理效果ATE的定义为

个体 <math> i </math> 的处理效应定义为 <math> y_{1}(i)-y_{0}(i) = \beta (i) </math> 。在一般情况下，这种处理效果在个体之间是不一样的。平均处理效果<math> \textbf{ATE} </math>的定义为

:<math>\text{ATE} = \frac{1}{N}\sum_i (y_{1}(i)-y_{0}(i))</math>

:<math>\text{ATE} = \frac{1}{N}\sum_i (y_{1}(i)-y_{0}(i))</math>