 `\(Y^0_i =\)` outcome for person `\(i\)` if `\(T_i = 0\)` (don't take Advil).

The **treatment effect** for person `\(i\)` is:
`$$\text{Effect}_i = Y^1_i - Y^0_i.$$`

--

**The Fundamental Problem of Causal Inference:** Only one potential outcome is ever observable for each person.

`$$Y_{i} =
\begin{cases}
Y_{i}^{1} &amp; \text{if } T_{i}=1\\
Y_{i}^{0} &amp; \text{if } T_{i}=0
\end{cases}$$`
The other one is a **counterfactual** -- what *would* have happened had `\(T_i\)` been different.

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# Average T