Question: A well-known example of Simpson's Paradox, published by Bickel, Hammel, and O'Connell (1975), examined admission rates for men and women who had applied to graduate programs at the University of California at Berkeley. The actual breakdown of data for specific programs is confidential, but the point can be made with similar, hypothetical numbers. For simplicity, we will assume there are only two graduate programs. The figures for acceptance to each program are shown in Table.
a. Combine the data for the two programs into one aggregate table. What percentage of all men who applied were admitted? What percentage of all women who applied were admitted? Which sex was more successful?
b. What percentage of the men who applied did Program A admit? What percentage of the women who applied did Program A admit? Repeat the question for Program B. Which sex was more successful in getting admitted to Program A? Program B?
c. Explain how this problem is an example of Simpson's Paradox. Provide a potential explanation for the observed figures by guessing what type of programs A and B might have been.
