What is a back-door criterion in causal inference?

Instruction: Define the back-door criterion and provide an example of how it might be used in a study.

Context: This question assesses the candidate's understanding of the back-door criterion, a concept crucial for identifying valid causal paths and controlling for confounding variables in observational studies.

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In a causal DAG, a set Z satisfies the classical back-door criterion for treatment X and outcome Y if no member of Z is a descendant of X and Z blocks every path between X and Y that begins with an arrow into X. Blocking follows d-separation; it is not simply including every variable correlated with X or Y.

Suppose baseline resources C cause both program...

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