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I get stuck with this short text from the paper "Estimating Treatment effects with causal forests".

"This dataset exhibits two methodological challenges. First, although the National Study itself was a randomized study, there seems to be some selection effects in the synthetic data used here. As seen in Figure 1, students with a higher expectation of success appear to be more likely to receive treatment. For this reason, we analyze the study as an observational rather than randomized study. In order to identify causal effects, we assume unconfoundedness, i.e., that treatment assignment is as good as random conditionally on covariates (Rosenbaum and Rubin, 1983) {Yi(0), Yi(1)} ⊥⊥ Wi (given Xi) What I did not understand is the notion of being random conditional on covariates? Does it mean that even if the treatment is allocated based on some covariates, for example, as stated in the paper, still this assumption holds?
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kjetil b halvorsen
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  • Yes, you are correct. In a sentence: When there are no non-causal associations between the treatment and the outcome, we say there is unconfoundedness. The interpretation of "unconfoundedness" has be discussed extensively here [Unconfoundedness in Rubin's Causal Model- Layman's explanation](https://stats.stackexchange.com/questions/182222). – usεr11852 Jul 13 '21 at 02:31

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