The 25 women faculty members in the humanities division of a college have a mean salary of $65,000, whereas the five women faculties in the science division have a mean salary of $72,000. The 20 men in the humanities division have a mean salary of $64,000, and the 30 men in the science division have a mean salary of $71,000.
a. Construct a 2 × 2 table of sample mean incomes for the table of gender and division of college. Use weighted averages to find the overall means for men and women.
b. Discuss how the results of a one-way comparison of mean incomes by gender would differ from the results of a two-way comparison of mean incomes by gender, controlling for division of college. (This reversal of which gender has the higher mean salary, according to whether one controls division of college, illustrates Simpson’s paradox.)