Null hypothesis test on sample from a logistic regression


I'm a bit confused on this matter, and was hoping someone out there could help. Also new to the forum.

I created a logistic regression on population P. What I want to do, now, is test whether a subset S of the population is truly a "random" subset (i.e. I have selected these observations based on a characteristic, and I want to test whether this characteristic has an effect on the dependent variable outside the factors that I included in the model).

I know that for a linear regression, all I would have to do is find the standard error of the sample and then do a null hypothesis test, but I can't figure out the equivalent analysis for a logistic regression. Any ideas?