Context, Goal: To estimate the quantitative effect of the treatment on a continuous dependent variable, while controlling for another continuous variable.
I have one sample each from a test (n=918) and control (n=2,048) group. There is another variable, let's call it weight. The distribution of weight is arbitrary and very different among test and control groups (long-tailed, actually).
I need to estimate the difference in means between the test and control groups, while controlling for weight.
This is what I've come up with:
- Obtain kernel density estimate (KDE) to approximate the distribution of weight in the test group.
- Use rejection sampling on the control group to generate sample sets. Each sample set would therefore have the same distribution of weight as in the test group.
- Generating large number of such sample sets would provide confidence limits, apart from expected value of the distributed variable - kind of like a bootstrap.
- Is this a valid approach? The only other place I've seen a similar idea is this question.
- Is there a better alternative? Better could be simpler, more practical, more rigorous, etc.
- Would this method work if the sample size of the control group were much less relative to the test group?