§ Simpson's Paradox

• 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.