The American Association of University Professors (AAUP) reports yearly on faculty salaries for all types of higher education institutions across the United States. The following table lists the mean salary, in thousands of dollars, of full-time instructional faculty on nine-month contracts at four-year public institutions of higher education in 2010, by gender and academic rank. Regard salary as the response variable, gender as the explanatory variable, and academic rank as the control variable.

a. Find the difference between men and women faculty members on their mean salary
(i) Overall and
(ii) After controlling for academic rank.
b. The overall difference between the mean salary of men and women faculty members was larger than the difference at each academic rank. What could be a reason for this? (Simpson€™s paradox does not hold here, but the gender effect does weaken when we control for academic rank.)

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Mean Salary (Thousands of Dollars) for Men and Women Faculty Members Academic Ranlk Gender Professor Associate Assistant Instructor Overall Men Women 109.2 96.2 77.8 2.7 66.1 61.8 46.0 46.9 84.4 68.8