A Universe of Sorts

The example which made simpson's paradox click for me was the extreme case.
Suppose department E hires every woman but only half the men ( E for every), while department N hires neither men nor women.
So in each department, women are either advantaged (as in E) or are on-par (as in N).
Suppose we have 100 men and 100 women.
Let 90 men apply for E and 10 men apply for N. In total, 45 men are accepted (90/2 + 0).
Let 10 women apply for E and 90 women apply for N. In total, 10+0 women are accepted.
Thus, it appears as if only 10 women are selected to 45 men, implying some kind of bias.
In reality, all departments are pro women hiring. The majority of women apply to the deparment Nwhich is hard to get into , thereby making it appear as if the institute ( E and N combined) are against women hires.
The information that is lost is that of the split up of men and women who apply to E and N.

§ Simpson's Paradox