How to calculate variance of binomial variable where base (n) is binomial also


New Member

I have a survey that collects data from each respondent on gender and also on attitudes.

We don't know in advance how many men or women will be identified.

We then ask attitudinal questions of each and wish to test for differences between the male and female groups.

It seemed clear that the base for each group (number men, number of women in total) was itself random and that this needed to be taken into account when estimating the variance of estimated proportions calculated on each gender group.

Also I thought there will be a negative correlation between the size of the male and female groups. Is there a way of computing the variance in this scenario?

Best wishes,