Chapter 12, Problem 8CS

We conclude that department is associated with both gender and admissions. Therefore, department is a confounder for the relationship between gender and admissions. This means that it is possible that the differences m admissions rates between men and women may be due to differences in the departments they apply to: rather than to gender. To determine whether this is the case; we must look at the admissions rates for men and women m each department separately. The following six tables present these data.

Which of the following is the best explanation for the fact that the graduate admissions rate is lower for than for men?

1. The admissions process discriminates against women.
2. Women tend to apply to departments that are harder to get into.

The data set in this case study provides an example of a result known as Simpson’s Paradox. Simpson’s Paradox occurs when two variables in a contingency table are dependent, but the dependence vanishes or reverses when separate tables are made for each level of a confounder. The lesson to be learned is that lack of independence is not the same as causation. When reject the null hypothesis of independence in an observational study, it is possible that the result may be due to confounding. To determine whether a certain variable is a confounder, it is necessary to make a separate table for each value of the confounder.