2.167 An example of Simpson’s paradox. Mountain View University has professional schools in business and law. Here is a three-way table of applicants to these professional schools, categorized by sex, school, and admission decision:40

Business Law
Admit Admit
Sex Yes No Sex Yes No
Male 400 200 Male 90 110
Female 200 100 Female 200 200

  1. (a) Make a two-way table of sex by admission decision for the combined professional schools by summing entries in the three-way table.

  2. (b) From your two-way table, compute separately the percents of male and female applicants admitted. Male applicants are admitted to Mountain View’s professional schools at a higher rate than female applicants.

  3. (c) Now compute separately the percents of male and female applicants admitted by the business school and by the law school.

  4. (d) Explain carefully, as if speaking to a skeptical reporter, how it can happen that Mountain View appears to favor males when this is not true within each of the professional schools.