Well,
I tried the suggested syntax with aweights and got it to work. The problem
is that I AM interested in significance levels. I tried using fweights and
iweights but the command does not work (just like with pweights).
I also tried using the svy command(s). The basic suite of svy commands are
do not allow correlations. But I did find a command online that allows
correlations using the svy command: findit corr_svy. After setting up the
svy command suite with my weights (using svyset) and downloading the
corr_svy command, I ran the corr_svy command and compared it with the
results from the [aw=wights] command.
The results are the same.
In what sense are they the same? I would expect the correlations to be the
same, but not the confidence intervals/ significance tests. Here is an
example: