Simpson's paradox

Simpson's paradox occurs when adding or removing a coefficient changes the results of analysis and is important for regressions. The 1973 Graduate School admission data from UC-Berkeley illustrates this point. At first glance, it appears females are less likely to be admitted to graduate programs. However, including Department as a coefficient causes gender's significance to disappear. As it turns out, prospective female students applied to more competitive programs than males.

Data note: When looking at the data, you are provided with four columns: Dept, Gender, Admitted, and Rejected. You can build a "binomial" glm() by binding the Admitted and Rejected columns.