I am trying to measure the effect of a treatment on a group which has not been randomly selected. I am using the propensity score matching method to compare the treated group to a balanced non treated group. I have done this using the R package "Matching" and have got an estimate of effect with an associated standard error.

The package measures the effect of treatment using a paired t-test. but my question is, what does the standard error mean if i am not trying to infer a treatment effect across a hypothetical treatable population, only the effect on that treated group.

It seems like I have a treated group which is a population and a control group which I think of as a sample. Would the distribution of differences between treated and non treated, be a sampling distribution? Or should I run the matching process many times and get my own distribution of average differences?

Hope I am making sense, thankyou for you help