7.11 Sex discrimination.

The data in Table 7.11 concern salary and other characteristics of 
all faculty in a small Midwestern college. The data have collected 
for presentation in legal proceedings for which discrimination 
against women in salary was at issue. All persons in the data hold 
tenured or tenure track positions; temporary faculty are not 
included. The data were collected from personnel files, and 
consist of the following quantities:
    
(1) case no
(2) Sex,  coded 1 for female and O for male 
(3) Rank, coded 1 for Assistant Professor,
                2 for Associate Professor
                3 for Full Professor
(4) Years = Number of years in current rank
(5) Degree = Highest degree, coded 1 if Doctorate, 0 if Masters
(6) YearsOut = Number of years since highest degree was earned
(7) Salary = Academic year salary in dollars


Exercises

7.11.1  Obtain a test of the hypothesis that salary adjusted for 
years in current rank, highest degree, and years since 
highest degree is the same for each of the three ranks, 
versus the alternative that the salaries are not the same

7.12.2  Using all the variables, show by suitable diagnostics 
the need to transform the response, salary, to some other 
scale, and suggest an appropriate transformation.

7.11.3  After transforming the response, test for nonconstant 
variance (a) as a function of salary and (b) as a function of 
the sex indicator.

7.11.4  Test to see if the sex differential in transformed 
salary is the same in each rank.

7.11.5  Using all the predictors, analyze these data with regard 
to the question of differential salaries for men and women 
faculty, and summarize your results in a fashion that might 
be useful in court.

7.11.6  Finkelstein (1980), in a discussion of the use of 
regression in discrimination cases, wrote, " . . . [a] 
variable may reflect a position or status bestowed by the 
employer, in which case if there is discrimination in the 
award of the position or status, the variable may be 
'tainted'." Thus, for example, if discrimination is at work 
in promotion of faculty to higher ranks, using rank to adjust 
salaries before comparing the sexes may not be acceptable to 
the courts.  Fit exactly the same model you found in 7.11.5, 
except leave out the effects of rank. Summarize and compare 
the results of leaving out rank effects on inferences 
concerning differential in pay by sex. 

Source: Weisberg, S. Applied Linear Regression, 2nd Edn. Wiley, 
New York, 1985.