II. Faculty Salary Equity Analysis

A. Brief Description of Average Faculty Salary Differentials by Gender and Ethnicity

The first three tables reported in this section are intended to provide a very brief indication of the variation in average 2002 yearly salaries across ethnic and gender groupings of St Cloud 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.

1. Faculty Salary By Gender

Table 1 shows a $5,915 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 2002 Salary by Gender

M/F	Mean	N	Std. Dev
F	51211	271	10822
M	57126	382	12696
Total	54671	653	12296

2. Faculty Salary By Gender and Rank

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 Instructor, Assistant Professor, Associate Professor and Professor ranks, male salaries are on average higher than the female averages.

Table 2. Average 2002 Salary by Rank and Gender.

rank	M/F	Mean	N	Std. Dev
professor	F	61867	83	7294
	M	66820	167	8543

associate professor	F	53851	64	5911
	M	56877	75	8726

assistant professor	F	46399	82	5153
	M	47831	110	7782

instructor	F	35526	42	4430
	M	37863	30	5010

3. Faculty Salary By Gender and Ethnicity

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 any other protected class, with the exception of Asian males.

Table 3. Average 2002 Salary by Ethnicity-Gender

ethnicity-gender	Mean	N	Std. Dev
white female	51718	233	11142
african amer female	*	1
asian female	49933	17	8132
hispanic female	45772	8	10439
native amer female	*	3
white male	57570	297	12755
african amer male	53614	19	10330
asian male	61767	39	13026
hispanic male	47285	8	6051
native amer male	*	3
unknown	47484	22	7823
Total	54671	653	12296

* Data are omitted if less than five faculty members within a grouping.

B. Promotion to Academic Rank

We note that this analysis uses current data patterns within campus to assess odds ratios for promotion. This analysis did NOT examine actual rates of promotion acceptance and rejection within a campus, as this data were not available for analysis. That is, we analyzed only the current distribution of faculty within ranks, broken out by ethnicity-gender. For example, at St Cloud there are 77 White male Assistant Professors and 53 White male Associate Professors, with corresponding odds of 53/77 (=0.688) of moving from Assistant to Associate rank. For White females there are 60 Assistants and 60 Associates, with corresponding odds of 60/60 (1.0) of being Associates. The “odds ratio” of White females to White males getting promoted from Assistant to Associate is then (1.0)/(0.688) = 1.453; that is, White female odds are 145.3% of the White male odds. The multinomial Logistic regression model adjusts these odds ratios to take into account the effects of other variables that might factor into promotion decisions, such as highest degree, previous experience, length of service, etc. When these control variables were entered into the Multinomial logistic regression model the odds ratio improved slightly, from 1.453 to 1.865 (see Table 4 below).

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.

Six minority dummy variables – African American males, White females, Asian males, Asian females, 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. black + female + associate professor), some minority groupings are combined into the Under-represented categories.

Table 4. Odds of Promotion to Higher Rank by Gender and Ethnicity

		Sig.	Exp(b)=Odds Ratio
assistant to associate	White female to White male	0.030	1.865
assistant to associate	Asian female to White male	0.566	0.621
	Under-rep female to White male	0.888	1.185
	Under-rep male to White male	0.885	1.139
	Afr Amer male to White male	0.608	1.420
	Asian Male to White male	0.101	2.352

associate to professor	White female to White male	0.248	0.731
associate to professor	Asian female to White male	0.403	2.135
	Under-rep female to White male	0.897	0.813
	Under-rep male to White male	0.622	1.635
	Afr Amer male to White male	0.182	0.414
	Asian male to White male	0.871	0.923

Table 4 shows the odds of promotion and associated statistical significance levels for six protected classes as compared to White males. There is no analysis for promotion from Instructor to Assistant Professor since there is “complete separation” in the data: that is, holding a Doctoral degree completely predicts promotion at this step. Only Asian females have lower odds of promotion from Assistant to Associate. From Associate to Professor, however, Asian females have better odds than the corresponding White male category, although neither coefficient is statistically significant. White females have lower odds of promotion from Associate to Professor than corresponding White male category, although the coefficient is not statistically significant.

There is no statistically significant evidence from this analysis to indicate that the Academic Rank variable is “tainted.” However, this finding will examined further below when the Total Population Regression Model is estimated after dropping the Academic Rank variable.

C. Controlling Salary For Structural Factors: Multiple Regression Analysis

1. Total Population Salary Analysis – with and without the Academic Rank variable.

Table 5 reports the estimated regression equation and auxiliary statistics for the Total Population Analysis (N=653). In this model, the dependent variable is 2002 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. Since there are insufficient numbers of Native American females (N=3) to use as a separate category, they were combined with the African American females (N=4) to form an Under-represented females category (N=7). Similarly, the Native American males (N=3) were combined with the Hispanic males (N=8) to form an Under-represented males category. There are sufficient White females (N=233), Asian females (N=17), and Hispanic females (N=8) for separate variables. African American males (N=19) and Asian males (N=39) were also entered separately as variables. 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 an increase in annual salary of $575, all other variables in the regression model being equal. For continuous variables, such as Years since Highest Degree, the corresponding unstandardized coefficient ($297) indicates how much each additional unit (here, a year) is worth, on average.

Table 5. Total Population Model With Ethnicity-Gender Variable.


	Unstandardized		Standardized	t	Sig.	Collinearity
	B	Std. Error	Beta	t	Sig.	Tolerance	VIF
(Constant)	55295	836		66.163	0.000

ACCTG	12952	1300	0.153	9.965	0.000	0.702	1.424
ALHEL	2002	1457	0.020	1.374	0.170	0.777	1.287
ARTFI	2553	1494	0.029	1.709	0.088	0.572	1.749
BIOLO	2816	1027	0.047	2.741	0.006	0.556	1.800
CHEMS	1491	1333	0.017	1.118	0.264	0.717	1.394
CISCS	12890	1040	0.220	12.394	0.000	0.525	1.905
COUED	3118	1284	0.037	2.428	0.015	0.719	1.390
COUNS	578	1595	0.005	0.363	0.717	0.808	1.237
CRMJS	2748	1372	0.030	2.002	0.046	0.732	1.365
CULTR	1880	1242	0.024	1.514	0.131	0.637	1.571
ECONO	6910	1234	0.087	5.599	0.000	0.684	1.463
EDCAD	2791	1323	0.032	2.110	0.035	0.729	1.372
EDCGN	1266	930	0.026	1.362	0.174	0.449	2.228
EDCSP	3185	1367	0.035	2.330	0.020	0.738	1.354
(ENGLISH)
ENGIN	13878	1352	0.158	10.264	0.000	0.698	1.433
FINAN	17319	1475	0.173	11.742	0.000	0.759	1.318
GEOGR	841	1367	0.009	0.615	0.539	0.739	1.354
HISTY	941	1396	0.010	0.674	0.500	0.708	1.412
LANGS	-389	1331	-0.004	-0.292	0.770	0.720	1.388
LIBRY	1540	1029	0.027	1.497	0.135	0.504	1.983
MARKT	14585	1317	0.172	11.076	0.000	0.684	1.462
MATHM	1740	939	0.035	1.852	0.065	0.469	2.133
MEDIA	3389	1375	0.037	2.464	0.014	0.729	1.371
MNGMT	14118	1233	0.178	11.453	0.000	0.685	1.459
MUSIC	-237	1167	-0.003	-0.203	0.839	0.646	1.547
PHILO	-260	1298	-0.003	-0.200	0.842	0.704	1.420
PHYED	1341	1139	0.026	1.177	0.240	0.333	2.999
PHYSC	3259	1106	0.049	2.946	0.003	0.598	1.671
POLSC	2995	1717	0.025	1.744	0.082	0.796	1.256
PSYCH	2203	1439	0.023	1.531	0.126	0.726	1.377
SOCAN	261	1054	0.004	0.248	0.804	0.565	1.769
SOCWK	3647	1593	0.035	2.289	0.022	0.722	1.386
SPECH	-715	1049	-0.012	-0.681	0.496	0.570	1.754
TECHN	2245	1543	0.021	1.455	0.146	0.769	1.300
THETR	-421	1643	-0.004	-0.256	0.798	0.762	1.313

(Professor)
Associate Professor	-5522	956	-0.184	-5.776	0.000	0.163	6.153
Assistant Professor	-10821	1156	-0.401	-9.360	0.000	0.090	11.145
Instructor	-18504	1607	-0.472	-11.518	0.000	0.098	10.174

(tenured)
probationary	4560	774	0.161	5.891	0.000	0.221	4.529
non-tenure track	-1950	1460	-0.021	-1.336	0.182	0.647	1.545
fixed term	1662	979	0.051	1.697	0.090	0.183	5.476
2yfixtrm	5768	1915	0.058	3.012	0.003	0.450	2.223
4yfixtrm	6010	1817	0.057	3.308	0.001	0.555	1.802

(Doctorate)
Special term	-2716	956	-0.048	-2.842	0.005	0.568	1.761
MA + Special non-term	-1851	761	-0.059	-2.432	0.015	0.283	3.538
Bachelors	-1446	1417	-0.020	-1.021	0.308	0.418	2.395

Prior exp	297	44	0.118	6.700	0.000	0.533	1.875
YRS since Hi Degree	76	36	0.058	2.125	0.034	0.221	4.535
YRS current rank PROF	424	118	0.216	3.596	0.000	0.046	21.800
YRS current rank PROF sqd	28	6	0.189	4.625	0.000	0.098	10.162
YRS current rank ASSOC	555	83	0.151	6.708	0.000	0.325	3.075
YRS current rank ASSIST	384	85	0.091	4.509	0.000	0.408	2.452
YRS current rank INSTR	133	250	0.012	0.531	0.595	0.312	3.202
Other MNSCU years	374	56	0.168	6.639	0.000	0.256	3.904

(white male)
white female	575	397	0.022	1.447	0.149	0.687	1.457
asian female	-325	1060	-0.004	-0.306	0.760	0.873	1.145
hispanic female	42	1513	0.000	0.028	0.978	0.899	1.113
under-rep female	2202	1635	0.018	1.347	0.179	0.878	1.139
african amer male	463	1007	0.006	0.460	0.646	0.868	1.152
asian male	585	761	0.011	0.769	0.442	0.765	1.307
under-rep male	-1339	1317	-0.014	-1.016	0.310	0.866	1.155
unknown	746	962	0.011	0.775	0.439	0.826	1.211

Reference categories: english, professor, tenured, doctorate, and white male shown in parentheses.

Six of the last seven variables in Table 5 indicate the effects of being in various protected classes, all other variables in the equation being held constant. The last variable, Unknown, was included to ensure that the reference category for all comparisons was strictly the White male category. None of the coefficients for the protected categories is statistically significant.

The Non-Terminal Specialist degrees were removed from the Specialist category and merged with the Non-Terminal Masters degree category. Thus, the Terminal Degree dummy variable, which was extremely multicollinear when entered into this equation, could be removed since it is essentially contained in the new highest degree codings.

The initial Total Population Model was estimated with squared terms for each of the years-in-rank and other time variables (Other MNSCU years, Prior experience, and Years since highest degree) included. All of the time variables were mean-centered and then squared to try to lessen the effects of multicollinearity that commonly occurs when squared terms are introduced into the regression model. These squared terms are useful in assessing non-linearities in the corresponding variables when they are used to predict current salary. Salary is commonly non-linearly related to such variables as age and time in rank, for example, where the squared term is usually negative, corresponding to a leveling off or even decrease in the relationship of the corresponding variable to salary after a substantial period of time. In the context of faculty salary prediction, the sign, magnitude and statistical significance of the squared terms are important in assessing whether salary “compression” has occurred for any group of individuals. Salary compression for professors with many years is rank is not uncommon.

Squared terms corresponding to each of the time-related variables were included in the initial run of the regression model (after being centered on their means). Only the squared term associated with Years in Current rank for Professor was statistically significant, and it is positive, indicating that faculty with many years in this rank are actually doing better towards the end of their careers. The other squared terms were not significant and caused severe multicollinearity problems with the associated variable, and so they were dropped from the model.

There is no evidence of salary compression from this squared time-variable analysis.

The positive coefficients for probationary and the various fixed term appointment statuses reflect the fact that the faculty in these statuses are either paid more on average than their tenured counterparts, and/or have substantially less years of service on average.

The last column in Table 5 reports the Variance Inflation Factor (VIF) for each predictor variable. This number indicates whether redundancy amongst the predictor variables is affecting the statistical significance levels of each of them. The VIFs associated with the Academic Rank set of variables suggest a slight problem with multicollinearity. However, all of these variables are very statistically significant and they are also substantively very important, so they were kept in the model.

Table 6 shows 89.3% (adjusted R-square) of the variance in annual salaries is explained by the structural variables in the above equation (Model 1). Table 6 also indicates the effects of simultaneously introducing all five ethnicity/gender variables as a “block” into the regression equation with only the structural variables initially included (Model 2). The “R Sq Change” column indicates that an additional 0.1% (.001) of the variance in annual salary is explained by adding these four variables after controlling for the set of structural variables, and this increase is not statistically significant (sig. F Change = 0.623).

Table 6. Variance Explained in 2002 Salary by Structural and Ethnicity-gender Variables.

Model	R	R Sq	Adj R Square	Std. Err of Est	Change Statistics
Model	R	R Sq	Adj R Square	Std. Err of Est	R Sq Change	F Change	df1	df2	Sig. F Change
1	0.950	0.902	0.893	4,025.357	0.902	101.590	54	598	0.000
2	0.950	0.903	0.893	4,031.365	0.001	0.777	8	590	0.623

To further check on “taint” in the rank variable, the Total Population model was re-run without the rank variable. If the rank variable is masking bias in the protected classes’ coefficients, those coefficients should be reduced in magnitude after rank is dropped. The coefficient for Hispanic females decreased from $42 to -$835, although this latter coefficient is still not statistically significant. However, changes in most of the other coefficients are both positive and not significant. Only the decrease for Hispanic females is suggestive of some masking of bias by the rank variable.

Table 7. Total Population Model without the Academic Rank variable.

	Unstandardized		Standardized	t	Sig.	Collinearity
	B	Std. Error	Beta	t	Sig.	Tolerance	VIF
(Constant)	51895	840		61.791	0.000

All other variables except rank

white female	639	440	0.025	1.450	0.147	0.689	1.451
asian female	310	1171	0.004	0.265	0.791	0.881	1.135
hispanic female	-835	1674	-0.007	-0.499	0.618	0.904	1.106
african amer male	232	1117	0.003	0.208	0.836	0.870	1.149
asian male	1363	841	0.026	1.621	0.106	0.772	1.296
unknown	837	1063	0.012	0.787	0.432	0.833	1.200
under-rep female	2262	1814	0.019	1.247	0.213	0.878	1.139
under-rep male	-476	1455	-0.005	-0.327	0.744	0.875	1.143

2. Natural Log of Salary Regression Model

In this model the dependent variable is the transformed variable, the natural logarithm of salary. Now, the unstandardized regression coefficients are no longer interpretable in terms of dollar amounts. Rather, unstandardized coefficients with small absolute values can be thought of as the proportions by which a salary changes for a one unit change in the corresponding predictor variable. If these coefficients are multiplied by 100, they can then be interpreted as approximate percentage changes. Thus, the coefficients associated with the various gender/ethnicity categories reveal the (approximate) percentage differences between each dummy variable and its reference category, after all the other variables have been controlled for.

The advantage of examining percentages rather than raw dollar disparities, as in the Total Population model, lies in the perspective of “return on investment” widely used by economists. If a regression coefficient for the Total Population model suggests that one discipline receives on average $1,000 more per years than the reference discipline, the corresponding Natural Log of Salary regression coefficient indicates what the corresponding “return on investment” is in choosing that discipline over the reference discipline. That is, with no baseline to compare it to, it is hard to tell if $1,000 is a “good” or “poor” return, but if it is 15% it would likely be considered a good investment.

Table 8 indicates that none of the other protected classes’ coefficients is significantly different from the White males reference category. The differences range from -0.2% (Asian female) to 5.1% (Under-represented females).

Table 8. Natural Log of Salary Model With Ethnicity-Gender Variables


	Unstandardized		Standardized	t	Sig.	Collinearity
	B	Std. Error	Beta	t	Sig.	Tolerance	VIF
(Constant)	10.903	0.015		726.453	0.000

ACCTG	0.243	0.023	0.153	10.399	0.000	0.702	1.424
ALHEL	0.042	0.026	0.022	1.603	0.110	0.777	1.287
ARTFI	0.051	0.027	0.031	1.906	0.057	0.572	1.749
BIOLO	0.062	0.018	0.056	3.385	0.001	0.556	1.800
CHEMS	0.038	0.024	0.023	1.577	0.115	0.717	1.394
CISCS	0.246	0.019	0.224	13.161	0.000	0.525	1.905
COUED	0.072	0.023	0.045	3.121	0.002	0.719	1.390
COUNS	0.015	0.029	0.007	0.507	0.612	0.808	1.237
CRMJS	0.063	0.025	0.037	2.561	0.011	0.732	1.365
CULTR	0.043	0.022	0.030	1.939	0.053	0.637	1.571
ECONO	0.138	0.022	0.093	6.235	0.000	0.684	1.463
EDCAD	0.061	0.024	0.037	2.587	0.010	0.729	1.372
EDCGN	0.037	0.017	0.041	2.244	0.025	0.449	2.228
EDCSP	0.066	0.025	0.039	2.700	0.007	0.738	1.354
ENGIN	0.257	0.024	0.156	10.599	0.000	0.698	1.433
FINAN	0.314	0.026	0.168	11.849	0.000	0.759	1.318
GEOGR	0.028	0.025	0.016	1.121	0.263	0.739	1.354
HISTY	0.023	0.025	0.013	0.910	0.363	0.708	1.412
LANGS	-0.004	0.024	-0.003	-0.182	0.856	0.720	1.388
LIBRY	0.036	0.018	0.034	1.951	0.052	0.504	1.983
MARKT	0.256	0.024	0.161	10.822	0.000	0.684	1.462
MATHM	0.040	0.017	0.042	2.350	0.019	0.469	2.133
MEDIA	0.074	0.025	0.043	2.995	0.003	0.729	1.371
MNGMT	0.253	0.022	0.170	11.429	0.000	0.685	1.459
MUSIC	-0.002	0.021	-0.002	-0.111	0.912	0.646	1.547
PHILO	0.003	0.023	0.002	0.119	0.906	0.704	1.420
PHYED	0.033

I. Executive Summary

Faculty Salary Analyses Highlights