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#causality #statistics
Exchangeability means that the treatment groups are exchangeable in the sense that if they were swapped, the new treatment group would observe the same outcomes as the old treatment group, and the new control group would observe the same outcomes as the old control group.
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#causality #statistics
The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), within levels of 𝑋 , they are not associated
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Flashcard 7070797663500

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The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), within levels of 𝑋 , they are not associated. In other words, there is no [...-ing?] within levels of 𝑋 because controlling for 𝑋 has made the treatment groups comparable.
Answer
confounding

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an> The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), within levels of 𝑋 , they are not associated. In other words, there is <span>no confounding within levels of 𝑋 because controlling for 𝑋 has made the treatment groups comparable. <span>

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This non-causal association flows along the 𝑇 ← 𝑋 β†’ π‘Œ path
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Flashcard 7070801071372

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We do not have [...] in the data because 𝑋 is a common cause of 𝑇 and π‘Œ . We illustrate this in Figure 2.3. Because 𝑋 is a common cause of 𝑇 and π‘Œ , there is non-causal association between 𝑇 and π‘Œ . This non-causal association flows along the 𝑇 ← 𝑋 β†’ π‘Œ path; we depict this with a red dashed arc
Answer
exchangeability

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We do not have exchangeability in the data because 𝑋 is a common cause of 𝑇 and π‘Œ . We illustrate this in Figure 2.3. Because 𝑋 is a common cause of 𝑇 and π‘Œ , there is non-causal association between 𝑇 and π‘Œ . This no

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Flashcard 7070802906380

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The [...] assumption is used in Equation 2.3. We will talk more about Equation 2.4 when we get to Section 2.3.5. Another perspective on this assumption is that of exchangeability.
Answer
ignorability

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The ignorability assumption is used in Equation 2.3. We will talk more about Equation 2.4 when we get to Section 2.3.5. Another perspective on this assumption is that of exchangeability.

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Flashcard 7070805527820

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Exchangeability means that the treatment groups are exchangeable in the sense that if they were [...], the new treatment group would observe the same outcomes as the old treatment group, and the new control group would observe the same outcomes as the old control group.
Answer
swapped

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Exchangeability means that the treatment groups are exchangeable in the sense that if they were swapped, the new treatment group would observe the same outcomes as the old treatment group, and the new control group would observe the same outcomes as the old control group.

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Flashcard 7070807362828

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We get the average treatment effect (ATE) 4 by taking an average over the [...]s: 𝜏 , 𝔼[π‘Œ 𝑖 (1) βˆ’ π‘Œ 𝑖 (0)] = 𝔼[π‘Œ(1) βˆ’ π‘Œ(0)] , (2.2) where the average is over the individuals 𝑖 if π‘Œ 𝑖 (𝑑) is deterministic. If π‘Œ 𝑖 (𝑑) is random, the average is also over any other randomness
Answer
ITE

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We get the average treatment effect (ATE) 4 by taking an average over the ITEs: 𝜏 , 𝔼[π‘Œ 𝑖 (1) βˆ’ π‘Œ 𝑖 (0)] = 𝔼[π‘Œ(1) βˆ’ π‘Œ(0)] , (2.2) where the average is over the individuals 𝑖 if π‘Œ 𝑖 (𝑑) is deterministic. If π‘Œ 𝑖 (𝑑) is random, the average is also over any other ran

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Flashcard 7070812343564

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Identifibility

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Flashcard 7070814178572

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there is no reason to expect that the groups are the same in all relevant variables other than the treatment. However, if we control for relevant variables by conditioning, then maybe the [...] will be exchangeable. We will clarify what the β€œrelevant variables” are in Chapter 3,
Answer
subgroups

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span> there is no reason to expect that the groups are the same in all relevant variables other than the treatment. However, if we control for relevant variables by conditioning, then maybe the <span>subgroups will be exchangeable. We will clarify what the β€œrelevant variables” are in Chapter 3, <span>

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