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Can someone please explain how to read the unconfoundedness assumption. I'm unable to understand the symbols specifically the upside down "T".

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Generally, that "upside down T" indicates orthogonality or independence (or unconfoundedness?) and I would interpret that notation as saying that the random vector $(Y_i(0), Y_i(1))$ is (conditionally) independent of the random variable $W$ given $X_i$, or more verbosely, conditioned on knowledge of $X_i$. If the random variables are jointly continuous and thus have joint densities, we can write

$$f_{Y_i(0), Y_i(1), W \mid X_i = x}(y_0,y_1, w \mid X_i = x) = f_{Y_i(0), Y_i(1) \mid X_i = x}(y_0,y_1, \mid X_i = x)f_{W \mid X_i = x}(w \mid X _i= x)$$ telling us that the conditional pdf of $Y_i(0), Y_i(1), W$ given $X_i=x$ factors into the product of the conditional pdf of $Y_i(0), Y_i(1)$ given $X_i=x$ and the conditional pdf of $W$ given $X_i=x$ and this factorization holds for all values $x$ that $X_i$ might take on. It is worth keeping in mind that conditional independence does not imply unconditional independence. It is not necessarily the case that $f_{Y_i(0), Y_i(1), W}(y_0,y_1, w)$ factors into the product $f_{Y_i(0), Y_i(1)}(y_0,y_1)f_{W}(w)$.

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