MnSCU – Winona State University
1997 Salary Equity Analysis
March, 2003
Prepared by:
Thomas McMullen
Senior Consultant
Hay Group
Eric Jacobs
Consultant
Hay Group
Malcolm M. Dow
Professor Emeritus
Northwestern University
Table of Contents
I. Executive Summary .................................................................................................... 1
II. Faculty Salary Equity Analysis................................................................................... 2
A. Brief Description of Average Salary Differentials by Gender and Ethnicity.............. 2
1.... Salary By Gender................................................................................................. 2
2.... Salary By Gender and Rank.................................................................................. 2
3.... Salary By Gender and Ethnicity............................................................................ 2
B. Promotions to Academic Rank................................................................................... 3
C. Controlling Salary For Structural Factors: Multiple Regression Analysis................. 5
1.... Total Population Salary Analysis ........................................................................ 5
2.... Natural Log of Salary Regression Model............................................................. 9
D. Individual-level Salary Differences: Regression Residuals..................................... 11
E. Summary................................................................................................................... 12
This statistical analysis of the Winona State faculty salary data used the Multiple Regression model to predict salaries based on a number of factors known to affect pay. Variables coding for gender and minority status were included in the analyses. No faculty performance measures were included.
The analyses indicate that none of the average salaries for protected classes are statistically significantly different from similarly situated White male faculty.
A highly statistically significant negative coefficient associated with the square of the Years in Current rank for Professors variable indicates salary compression issues for faculty with many years of service in this rank.
Forty one faculty had differences between actual salary and predicted salary (residuals) that were less than one standard deviation below the mean. Of these, 16 are in protected classes and 25 are White males.
A Multinomial Logistic Regression of the Academic Rank variable indicated that the odds of promotion to higher Rank for White males versus the five protected classes were not statistically significantly different from the corresponding Male categories. In addition, the Total Population Model without the academic Rank variable did not result in any significant amount of masking of bias in average salaries for protected classes by the rank variable. Thus, no “taint” in Rank was uncovered by these analyses.
The first three tables reported in this section are intended to provide a very brief indication of the variation in average 1997 yearly salaries across ethnic and gender groupings of Winona State faculty. Explaining as much of this variation in salary as possible, using additional background factors such as academic rank and length of service, is the focus of this report.
Table 1 shows a $5,491 shortfall in average annual salary for female relative to male faculty. Several factors that account for much of this difference will be discussed below.
Table 1. Average 1997 Salary by Gender
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|
Gender |
Mean |
N |
Std. Dev |
|
Male |
49143 |
177 |
10605 |
|
Female |
43652 |
125 |
8904 |
|
Total |
46870 |
302 |
10284 |
One major factor that affects faculty salary differences is Academic Rank. Table 2 reports average annual salaries broken out by Gender and Rank. At the Assistant Professor, Associate Professor and Professor ranks, male salaries are on average higher than the female averages. At the Instructor rank, on average females salaries are higher.
Table 2. Average 1997 Salary by Rank and Gender.
|
rank |
Gender |
Mean |
N |
Std. Dev |
|
Professor |
Male |
56400 |
92 |
5802 |
|
Female |
53207 |
40 |
5423 |
|
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|
|
|
|
|
|
Associate Professor |
Male |
46683 |
35 |
6542 |
|
Female |
44170 |
34 |
5013 |
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|
|
|
|
|
|
|
Assistant Professor |
Male |
39887 |
41 |
7253 |
|
Female |
37133 |
43 |
3537 |
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|
|
|
|
|
|
Instructor |
Male |
26697 |
9 |
2927 |
|
Female |
28709 |
8 |
2799 |
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|
|
|
|
|
Table 3 reports average salary differences broken out by a combination of Gender and Ethnicity. Again, this table shows substantial salary differences in average salaries across these groupings. The average salary for White males is higher than that of all other protected classes except Under-represented males.
Table 3. Average 1997 Salary by Ethnicity-Gender
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Ethnicity-Gender |
Mean |
N |
Std. Dev |
|
white female |
43621 |
117 |
8904 |
|
under-rep female |
44103 |
8 |
9513 |
|
asian male |
48446 |
11 |
6943 |
|
under-rep male |
51629 |
6 |
8656 |
|
white male |
49248 |
159 |
10769 |
|
Total |
46942 |
301 |
10225 |
Table 4 shows the estimated odds ratios of promotion from Assistant Professor to Associate Professor and from Associate Professor to Professor obtained using the Multinomial Logistic Regression model. The odds ratios were calculated after controlling for Highest Degree, Years of Prior Experience, and Length of Service. There are no promotions shown for Instructor to Assistant, since there is “complete separation” in the data, meaning that the Doctorate variable completely predicts this promotional step.
Odds ratios greater than 1.0 indicate a correspondingly greater likelihood for individuals in the indicated category in obtaining promotion to the next category. Conversely, odds less than 1.0 indicate less likelihood.
Five minority dummy variables – Females, White females, Asian males, Under-represented females and males – were included in predicting odds of promotion to higher rank. Because categorical modeling cannot handle groupings with very low frequency for combinations of attributes (e.g. African American + female + associate professor), some minority groupings had to be combined into the Under-represented categories.
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Table 4. Odds of Promotion to Higher Rank by Gender and Ethnicity |
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|
Sig. |
Exp(b)=Odds Ratio |
|
Instructor to Assistant |
Female to Male |
0.168 |
2.520 |
|
|
White Female to White Male |
0.260 |
2.145 |
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|
|
|
assistant to associate
|
White female to White male |
0.483 |
1.321 |
|
Under-rep Female to White male |
0.511 |
0.446 |
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|
|
Asian male to White male |
0.966 |
1.042 |
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|
Under-rep male to White male |
0.621 |
1.829 |
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associate to professor
|
White female to White male |
0.291 |
0.637 |
|
Under-rep female to White male |
0.415 |
2.836 |
|
|
|
Asian male to White male |
0.934 |
1.075 |
|
|
Under-rep male to White male |
0.173 |
0.197 |
Table 4 shows the odds of promotion and associated statistical significance levels for five protected classes as compared to White males. There is no analysis for promotion from Instructor to Assistant Professor for three protected classes, since there are no individuals in these classes to be promoted. Three protected classes have better odds of promotion from Assistant to Associate than the corresponding male categories, although no coefficient is statistically significant. None of the odds ratios for Associate to Professor is statistically significant.
In general, one or more of the control variables -- Doctoral degree, Length of Service, and Prior experience -- were statistically significant in each equation examined here.
Since none of the promotion odds coefficients for protected classes are statistically significant after the control variables are entered into the equations, there is no statistically significant evidence from this analysis to indicate that the Academic Rank variable is “tainted.” However, this finding will be further examined in the section below on the Total Population Model without the academic rank variable.
1. Total Population Salary Analysis
Table 5 reports the estimated regression equation and auxiliary statistics for the Total Population Analysis (N=302). In this model, the dependent variable is 1997 Annual Salary, and the predictor variables are all of the structural variables plus a set of dummy variables corresponding to ethnic minority and gender status. African American males (N=3) were combined with the Hispanic males (N=3) to form an Under-represented males category (N=6). Similarly, the African American female (N=1) was combined with the Asian (N=4) and the Hispanic (N=3) females to form an Under-represented females category. There are sufficient White (N=117) females for a separate variable. African American (N=1), Asian (N=4), Hispanic (N=2), and Native American (N=1) females were also combined into an Under-represented female category. The reference category is thus White males.
The first column of Table 5 shows the labels of each of the variables entered into the regression model. The first term (constant) can be ignored. Each of the other terms in the first column corresponds to either a “structural” variable or one of the ethnicity-gender variables.
The second column in Table 5 shows the “unstandardized coefficient” B associated with each variable, which indicates the average amount by which each faculty member’s salary increases (or decreases) for a one unit change in the corresponding variable, all of the other variables in the equation being held constant. In the case of a dummy variable, the one unit change is from the omitted reference category (coded as 0) to the corresponding category (coded as 1). So, for example, the coefficient for White females in the second column indicates that an individual moving from the “White male” category (coded as 0) to the “White female” category (coded as 1) would be expected to have a decrease (negative coefficient) in annual salary of $469, all other variables in the regression model being equal. For continuous variables, such as Years since Highest Degree, the corresponding unstandardized coefficient ($100) indicates how much each additional unit (here, a year) is worth, on average.
Table 5. Total Population Model With Ethnicity-Gender Variable.
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|
Unstandardized |
Standardized |
t |
Sig. |
Collinearity |
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|
B |
Std. Error |
Beta |
Tolerance |
VIF |
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|
(Constant) |
50423 |
1146 |
|
43.994 |
0.000 |
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|
ACCTG |
4827 |
1504 |
0.084 |
3.210 |
0.001 |
0.553 |
1.809 |
|
ARTFI |
-2281 |
1670 |
-0.036 |
-1.365 |
0.173 |
0.556 |
1.797 |
|
BIOLO |
-1 |
1344 |
0.000 |
0.000 |
1.000 |
0.580 |
1.723 |
|
CHEMS |
-664 |
1451 |
-0.011 |
-0.458 |
0.647 |
0.658 |
1.520 |
|
CISCS |
5932 |
1362 |
0.117 |
4.356 |
0.000 |
0.524 |
1.908 |
|
COUED |
-719 |
1827 |
-0.009 |
-0.393 |
0.694 |
0.737 |
1.357 |
|
ECONO |
2974 |
1538 |
0.047 |
1.933 |
0.054 |
0.656 |
1.524 |
|
EDCGN |
1309 |
1057 |
0.038 |
1.239 |
0.217 |
0.413 |
2.421 |
|
ENGIN |
10428 |
1837 |
0.130 |
5.676 |
0.000 |
0.728 |
1.373 |
|
HUMNS |
-2086 |
1310 |
-0.040 |
-1.593 |
0.112 |
0.611 |
1.636 |
|
LANGS |
-1029 |
1690 |
-0.014 |
-0.609 |
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