# Simpson paradox A paradox in statistics inference where grouping classes of results in opposite trend. For example, in 1973 there were 15,000 men and women applying to UCB. Per department there was even ratio of accepted men and women with slight advantage to women. But when grouping the departments and looking on the overall accepted applications, the results favor men. The reason was that women apply more to departments with low rate of acceptance while men apply to departments with high rate of acceptance. So, over whole, more women got rejected. Let say that department A acceptance rate is 50% and department B is 10%. Assume 100 men apply to A and 10 women apply to A, 10 men apply to B and 100 women to B. Assuming fair gender acceptance: 50 men and 5 women will be accepted to A, 1 men and 10 women will be accepted to B. Ignoring the departments the acceptance rate of men is $50+1/110=0.46$ vs. women acceptance rate of $5+10/110=0.13$ .This hints to gender inequality acceptance but we know they were exactly the same rate for man and woman for each department. Reference: [[@The pea and the sun]], [Wikipedia](https://en.wikipedia.org/wiki/Simpson%27s_paradox) ## Created 2024-01-05 14:09