The CSU Salary Equity Saga

Mary MeyerStatistics Dept, CSU

In May 2014, Rick Miranda asked me to be on a task force, together with Sue James and Sue Doe,to work with Laura Jensen and some IR staff to do a gender equity analysis of the salaries of regularfaculty. I got the data for FY2014 (and some earlier data) and did a fairly straight-forward statisticalanalysis (documented in the appendix to this saga). In short, I found that while no systematic salarydiscrepancies existed at the assistant and associate levels, once the effects of department, rank, yearssince degree and years at CSU were accounted for. However, there was a significant gap at the fullprofessor level, and the largest gap was in the college of Vet Med.

I presented the results to the committee, then to Rick in July. I wanted to present the results to thesenior women faculty group, but he asked me to hold off until they could talk to Vet Med and see whatthey had to say.

In early September I presented the results to the Diversity Symposium, which was also attended byLaura Jensen. Shortly after this, the Coloradoan had an article that implied CSU was really on topof equity issues, and mis-quoted Diana Prieto as saying there were no gender imbalances in salaries.At this point there were some emails from women faculty saying“we didn’t appreciate reading it in thepaper before ‘our group’ saw it/heard about i” – which I totally understand, but my input or analysiswas not consulted; I didn’t know about the article before it appeared.

Because of this, I decided to stop waiting for permission, and gave two presentations of the results. Ifelt strongly (and I expressed this to Rick and Laura and everyone else) that all faculty had a right toknow how their salaries compared with others in their department, rank, and seniority, and announcedI was willing to send people their predicted values and residuals, along with interpretation.

So, I re-ran the analysis without the gender variable, and saved predicted values to each faculty member.This is a “sort of average” (see appendix) salary for a regular faculty member, given department, rank,and seniority. I could then tell individuals that their salary was 8% under, or 3% over, this averagevalue.

Laura then made an IR website (now taken down) with the predicted values from the same (I think)analysis including the gender variable. (She called this predicted value a “median.”) This meant thatthe “median” given for women full professors was considerably less than the “median” for a man withthe same department, rank, and seniority. Of course, I didn’t know this at the time, but assumedthat she was providing the same information as I had been. Since she attended at least two of mypresentations, she certainly knew what I was doing.

Later that fall semester I met with Rick, Laura, and Dan Bush to discuss future analyses. I was willingto turn this job over to IR, because I had provided documentation of the model, the steps in the analysis,and the interpretation of the results. It’s not that complicated! However, in this meeting I emphasizedthat the analysis to determine if there is systematic gender inequity at CSU should be different fromthat for the individual salary equity exercise, for which IR provides data every year. We discussed theold method where there was a simple linear regression line for salary against years since degree, doneseparately for each department. We agreed that this was too simplistic, and talked about better ways todo it. We discussed some ideas, and I offered to be involved, but after that meeting I was not consultedagain.

Fast forward to last week. Here is an email that I sent on Thursday:

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Dear Laura, Dan, and Rick,

Yesterday I was given the attached photocopy of some pages documenting the individualsalary equity exercise that is performed annually. I have some questions/issues about theprocedure.

First, the analysis that I did had the very specific purpose of comparing salaries at CSUby gender. One of the first tenets of data analysis is that the method should be driven bythe purpose. However, the annual salary equity exercise has a quite different purpose. (Wediscussed this in that meeting in Rick’s office last fall.)

I feel like the statement that “a senior CSU Statistics faculty member took the lead ondevelopment of a new methodology” is inaccurate, because I had no input on how thisannual exercise is conducted. In fact, I have strong objections to what is described in thepages.

In my opinion, the calculation of the median salary (which is used as a target) should useonly rank, department, and years in rank, or if the latter is still not available, years sincedegree. Including years at CSU in the model means that the target salary for folks whohave been at CSU for a long time is considerably lower than the target for someone who hasarrived recently, all other things being equal. Does CSU really want to have a policy thatloyal faculty should be paid less?

Also, in the document, it says that gender is also included in the model. I assume that thisis a mistake!! Having lower targets for women would not only go against everything wevebeen talking about, but would (I hope) be illegal.

I have other questions about the methodology, but they are not policy-related. For example,are data from departments combined to determine the median relationships between salaryand seniority, or are these done individually by department? What if, as in computer science,the relationship between salary and years since degree is negative? Does the target decreasewith seniority as well, or is this held constant?

I would be happy to be involved with designing this annual exercise... I appreciate havinghad input with last year’s gender equity study. I don’t mean to complain or cause trouble, Ijust want this to be done right. I feel that including years at CSU in the target will adverselyaffect women more than men, and will also adversely affect those with families and ties tothe community.

Best, Mary

Well! It turns out that gender was included in the model, and that the target salaries for women wereless than for men, sometimes substantially less, all other things being equal. And equity raises weredeclined because of this. At this point Jean Opsomer, Jan Nerger, and I raised a big fuss.

This is also when I asked Laura about the IR interactive website, and she (unapologetically) statedthat yes, men’s medians were higher than women’s, because that’s what the model gave us. Becauseshe refused to see any problem with the website or the salary equity documents, that’s when I emailedthe senior women faculty list-serve.

Since then, as you know, the IR documents have been rescinded, the website has been taken down, andDiana Prieto is investigating.

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Technical Appendix

The Data

There are 1045 observations representing tenured or tenure track faculty at CSU, presented to me inan Excel file. The data set contains the following variables:

• The response variable is the nine-month salary. There are several pertinent variables in the Excelfile:

– ACTUAL SALARY, the yearly salary of the individual.

– BOS, the “basis of service.” For the AY2014 data, this was either 9 or 12, reflecting themonths of service for the year.

– NINE MONTH SALARY, calculated by IR. For the 9-month faculty, this is equal to actualsalary, but for the 12-month faculty, this is 81.8% of actual salary. I re-calculated the 9-monthsalary to be 75% of the actual salary for the 12-month faculty.

• GENDER, two levels

• RANK: The three ranks are assistant, associate, full.

• ASSIGNMENT DEPT: the department where the faculty member works. There are 54 depart-ments, with 8 faculty members in the smallest (Ethnic Studies) and 64 in the largest (ClinicalSciences).

• ASSIGNMENT COLLEGE: the college where the faculty member works.

• DEGREE YEAR: the year the faculty member received the PhD.

• YEAR CSU: number of years as faculty at CSU.

Analysis by Rank and Sex

The average nine-month salaries by gender and rank are:

• Female Assistant: $73,041.56

• Male Assistant: $78,123.09

• Female Associate: $79,320.14

• Male Associate: $86,406.27

• Female Full: $100,874.65

• Male Full: $117,569.93

To do a statistical analysis, we use the log of the salaries, because of the skewed distribution.

Let yi be the log(9-month-salary) for the ith faculty member, i = 1, . . . , 1045. Let

• r1i = 1 if the ith faculty member is a female assistant professor, and d1i = 0 otherwise

• r2i = 1 if the ith faculty member is a male assistant professor, and d2i = 0 otherwise

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• r3i = 1 if the ith faculty member is a female associate professor, and d3i = 0 otherwise

• r4i = 1 if the ith faculty member is a male associate professor, and d4i = 0 otherwise

• r5i = 1 if the ith faculty member is a female full professor, and d5i = 0 otherwise

• r6i = 1 if the ith faculty member is a male full professor, and d6i = 0 otherwise

We use the model:

yi = β1r1i + β2r2i + β3r3i + β4r4i + β5r5i + β6r6i + εi, i = 1, . . . , n,

where we assume that β1 is the “true average” log-salary for women assistant professors at CSU, and theother coefficients are defined similarly. The term εi is a “random error” or more accurately “variationthat is unexplained by gender and rank.”

The coefficients can be interpreted as follows: exp(β2 − β1) is the ratio of male assistant professorsalaries to female assistant professor salaries, across CSU. The estimates of these are:

• exp(β̂2−β̂1) = 1.059, meaning that male assistant professors make 5.9% more than female assistantprofessors.

• exp(β̂4 − β̂3) = 1.096, meaning that male associate professors make 9.6% more than femaleassociate professors.

• exp(β̂6 − β̂5) = 1.162, meaning that male full professors make 16.2% more than female full pro-fessors.

If the εi can be assumed to be independent and approximately normal with mean zero and commonvariance, then the p-values for various t-tests are valid. We perform three (separate) two-sided t-tests:

• H0 : β1 = β2 versus Ha : β1 6= β2: p = .045

• H0 : β3 = β4 versus Ha : β3 6= β4: p < .0001

• H0 : β5 = β6 versus Ha : β5 6= β6: p < .0001

The multiple R2 is .378, indicating that 37.8% of the variation in log(salary) at CSU is due to rank andgender.

Analysis by Rank and Sex, Controlling for Effect of Department

There is a lot of variation in salary among the 54 departments: the highest average 9-month salary is$143,461 (Marketing) while the lowest is $48,248 (Library). We can model the department effect bycreating 54 indicator variables for departments, and adding 53 of these to the above model. Supposedji = 1 if the ith faculty member is in department j, and dji = 0 otherwise, for j = 1, . . . , 54. Thenour model is

yi = β1r1i + · · ·+ β6r6i + α1d1i + · · ·+ α53d53i + εi, i = 1, . . . , n,

where now β1 is “true average” log-salary for women assistant professors in department #54, and β1+αj

is the true average log-salary for women assistant professors in the jth department, and ditto for otherrank/gender combinations. (I checked for interaction between the department and rank/gender, and it

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was insignificant. This means that the salary ratios for the gender/rank combinations are approximatelythe same across departments.)

The department effect is highly significant, with 81.0% of the variation in log-salary explained by rank,gender, and department. We can perform the same hypothesis tests to get p-values for the differencesin salary by gender, for each rank, after the department effect is controlled for:

• H0 : β1 = β2 versus Ha : β1 6= β2: p = .91

• H0 : β3 = β4 versus Ha : β3 6= β4: p = .81

• H0 : β5 = β6 versus Ha : β5 6= β6: p = .0002

After controlling for department, we find that there is no significant difference between male and femaleassistant professor salaries at CSU, and also no significant difference between male and female associateprofessor salaries. However, exp(β̂6 − β̂5) = 1.068, meaning that male full professors make 6.8% morethan female full professors, and this is quite significant as well as substantial, although the departmenteffect “explained” much of the discrepancy in full professor pay.

Analysis by Rank and Sex, Controlling for Effect of Department and Seniority

We have two measures of seniority in the data: years at CSU and years since degree. The average yearssince degree for female full professors is 25 years, compared to 28 years for male full professors. Weexpect pay to go up as one’s career progresses, so we need to account for seniority when comparingsalaries.

The relationship of log salary to years since degree would be linear if the salaries increased by approx-imately the same percentage every year. However, academic salaries tend to increase faster than this,with bumps for promotion, merit pay increases, and increases when the faculty member moves to adifferent university, or perhaps just threatens to. Using modern nonparametric methods, we can modelthis trend as simply “smooth and increasing,” to avoid problems with parametric mis-specification.

The relationship of log salary to years at CSU, once years since degree is controlled for, is actuallydecreasing. This is because faculty members who move typically receive large salary increases. Ournew model is:

yi = β1r1i + · · ·+ β6r6i + α1d1i + · · ·+ α53d53i + f1(x1i) + f2(x2i) + εi, i = 1, . . . , n,

where x1i is the years since degree for the the ith faculty member, and x2i is the years at CSU for thethe ith faculty member. The function f1 is smooth and increasing, while the function f2 is smooth anddecreasing. The estimates of the functions are shown in Figure 1.

Now, exp(β̂6 − β̂5) = 1.046, meaning that male full professors at CSU make 4.6% more than femalefull professors at CSU, after effects of department and seniority are accounted for. The p-value forH0 : β5 = β6 versus Ha : β5 6= β6 is p = .002, indicating rather strong significance. The multipleR2 tells us that 83.5% of the variation in log(salary) is explained by the predictors: rank, gender,department, and the two kinds of seniority.

Residual Analysis

Some standard residual plots are shown in Figure 2, showing heteroskedasticity with respect to therank/sex variable, and some left-skewness with heavy tailed residuals.

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Figure 1: Estimated effects of seniority on salary, using nonparametric constrained regression.

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Figure 2: Residual plots for final model.

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Figure 3: Plots of weighted residuals for final model, using weights from the rank/sex categories.

We can correct for the heteroskedasticity by weighting, using a weight vector equal to the inverse of thevariance of the residuals in each of the six rank categories. Plots of the weighted residuals are shownin Figure 3, showing a substantial improvement, but still slightly heavy-tailed. The results by genderare virtually the same as for the unweighted model; there is no difference in any of the conclusions.

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