Hi everyone,

My question is: when the weight in my data is post-stratification weight, how should I incorporate these weights into my calculation of bootstrap confidence intervals?

Example:
My data is collected through a stratified sampling framework. The number of observations within each strata in my sample is NOT proportional to the relative population size of each strata. So I have brought in post-stratification weights into my data. These weights are used in all of my original analyses.
Now I need to calculate bootstrap confidence intervals for my estimates. I have to do this manually by randomly sampling 100 samples (because of the specific analytic strategies that I adopt for my research).
Initially, I simply use
Code:
foreach boot of numlist 1(1)100 { // Bootstrapping with 100 replications
disp `boot'
set seed `boot'
gsample ,strata(stratavar)
}
After appending the 100 samples together, I calculate the mean of the statistic across the 100 samples. When calculating the mean, I imposed the post-stratification weights in my original data set. Interestingly, the mean of the statistic across the 100 samples seems to be substantially higher than my original estimate (which is derived also after imposing the post-stratification weights). I then tried gsample [w=weight], which yields an even higher sampling mean of my 100 samples.

Finally, I tried to drop weights from all my analyses. Now the mean of the statistic across the 100 samples is in line with my original unweighted estimate. So I feel I must have done something wrong. Can someone point it out where I did wrong?

So to reiterate my question: when the weight in my data is post-stratification weight, how should I incorporate these weights into my calculation of bootstrap confidence intervals?

Thank you!