I am helping a student with an analysis of a dataset with a fair bit of missing data and am exploring using multiple imputation.

There's nothing too elaborate in the analysis - the main components are to test for differences in proportions and calculate correlations. To that end prtest (one sample) and pwcorr don't work with mi estimate that I can see.

For the former is there an equivalence to running an intercept only logistic model and for the latter, could I effectively run a regress on the standardised versions of the variables (to obtain the same results as prtest and pwcorr, but on multiply imputed datasets)? Like in the following (just on the one dataset to illustrate):

Code:
sysuse auto, clear

* prtest vs logit-margins
prtest foreign == 0.5
logit foreign // p-value is test of difference of log-odds from 0?
margins // p-value is test of difference of probability from 0.5?

* pwcorr vs regress using z-scores
pwcorr weight length
egen weight_z = std(weight)
egen length_z = std(length)
reg weight_z length_z
reg length_z weight_z
Thanks,

Paul