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 data for specific programs is confidential, so we are using similar, hypothetical numbers. For simplicity, we assume there are only two graduate programs. The figures for acceptance to each program are shown in the following table:
a. Combine the data for the two programs into a single table. What percentage of all men who applied was admitted? What percentage of all women who applied was admitted? Which sex was more successful in the admissions process?
b. What percentage of the men who applied to program A did program A admit? What percentage of the women who applied to program A did program A admit? Repeat the question for program B. Which sex was more successful in getting admitted to program A? Into 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.