1
$\begingroup$

Page 259 of the book writes:

Suppose we look at the subpopulation of all units with $X_{i}=x ;$ within this subpopulation the difference in the distributions of the observed outcomes, between treated and control units, fairly represent the effects of the treatment in this subpopulation, because, within this subpopulation, the treated and control units are both random samples from that subpopulation.

Can someone help me understand "the treated and control units are both random samples from that subpopulation"? I am not quite convinced that this is the case.

In other words, if we have a sample that is also the entire finite population. Now we take a subsample by picking units whose covariate value is $X_i=x$. Is it necessarily true that this subsample is also a random sample from the subpopulation $X_i=x$?

Edit: Okay so I think Rubin has a finite sample perspective when he is writing this. Then "treated and control units with $X_i=x$" should just make up the subpopulation $X_i=x$ right?

Improve this question
$\endgroup$
1
  • $\begingroup$ Right. I would say if the treated and control units were randomly chosen in the entire population, they should be random in the subpopulation. $\endgroup$
    – Adrian Keister
    May 28, 2020 at 15:15

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.