# Compensation Analysis

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1 Appendix B: Section 3 Compensation Analysis Subcommittee: Bruce Draine, Joan Girgus, Ruby Lee, Chris Paxson, Virginia Zakian 1. FACULTY COMPENSATION The goal of this study was to address the question: are men and women on the Princeton faculty paid equally for equal work? To address this issue, Dr. Mark Killingsworth was commissioned to carry out a statistical analysis of salaries for the professorial staff, and was given access to the University's salary records for Dr. Killingsworth's report appears in Appendix C, Section 1; we summarize the principal results here. In compensation analyses one is primarily interested in relative salaries, and it is therefore natural to examine systematic differences in logarithm of salary, as the difference in the logarithms of two salaries is directly related to the ratio of the salaries. A first approach is to simply compare the mean log(salary) for male and female faculty. This corresponds to fitting a simple model with two adjustable coefficients (a 0 and D) ln S = a 0 + D G (model 1) to the salary data, where ln is natural logarith, S is salary, and the "gender variable" G=0 for males, and G=1 for females. In this model, the gender difference is the best-fit value of the coefficient D. The average female salary is exp(d) times the average male salary. The "percentage difference" between female and male salaries is [exp(d)-1] 100%; when D is negative the percentage difference is negative (women paid less than men). Figure 1 ( curve labeled model 1: gender only ) shows the percentage difference between salary of female faculty and the salary of male faculty, where the fit is to the salaries of all assistant, associate, and full professors employed by Princeton University (Divisions I-IV) for each of the years between 1991 and The error bars represent 1-σ uncertainties in the estimate for the fractional difference. The error bars can be thought of as 68% confidence intervals for the indicated quantity. The mean difference over this 11 year window is 22%. While the gap is narrowing with time, it is still considerable: In 2002, women, on average, earned 18% less than men. We expect salaries to vary with experience and accomplishment. Since the fraction of women in the Princeton faculty has been growing with time (and recent hires are on average younger), in any given year, female faculty members at Princeton have (on average) fewer years of experience than the male faculty. Experience and accomplishment are intangible, but would be Appendix B: Section 3 Compensation Analysis 21

2 expected to correlate with the number of years elapsed since award of a PhD. A simple model was considered where, for a given academic year, an individual's salary depends linearly and quadratically on years t since PhD, and also on gender: ln S = a 0 + a 1 t + a 2 t 2 + D G (model 2) Figure 1. Gender differences in salary (as a percentage) for all Princeton University faculty, for 11 years beginning October As discussed in the text, the gender differential is shown with no consideration of other factors (model 1: gender only), allowing for dependence of salary on the number of years since PhD and gender (model 2), dependence of salary on academic department, years since PhD and gender (model 3), and dependence on academic rank, academic department, years since PhD and gender (model 4). The error bars are inserted to indicate 68% confidence intervals. It is reasonable to suppose that any real gender bias is probably between models 3 and 4. Averaged over the 11-year period, the gender bias for all Princeton faculty does not exceed about -3.6%, but model 3 falls to -5% in 2001/2 and 2002/3. The dependence on t is not expected to be simple; the quadratic term is simply the first term beyond linear in a Taylor expansion. A least-squares fit was carried out using the actual salaries S to obtain the best-fit coefficients (a 0, a 1, a 2, D) for this model. The least-squares fitting procedure also provides a 1-σ uncertainty in the estimate of the gender coefficient D from the sample. The results are shown in Figure 1 as the curve labeled "model 2: gender + yrphd". The Appendix B: Section 3 Compensation Analysis 22

3 gender difference is reduced to about -8%, and appears to be relatively stable over the 11-year period. There are salary differences between departments, and women are not uniformly represented across the different departments: women constitute 30% of the humanities faculty, but only 8.8% of the engineering faculty. To see whether women's salaries are statistically different from those of their male colleagues in the same department, a model ln S = a 0 [dept] + a 1 t + a 2 t 2 + D G (model 3) was fitted to the salary data, where the coefficient a 0 was allowed to depend on the department. When this model is fitted to the data, the gender difference D is reduced, as seen in Figure 1: for the 11-year period, the mean difference is -3.6%. The use of years since PhD as an indicator for "experience and accomplishment" is obviously imperfect. Another indicator which one may consider is academic rank. To examine this effect, the salary data were fitted by a model ln S = a 0 [dept] + R[rank] + a 1 t + a 2 t 2 + D G (model 4) where the "rank coefficient" R=0 for assistant professors, with R[associate professor] and R[full professor] determined by least-squares fitting. This model results in quite small gender coefficients D for the entire Princeton faculty: the number varies from year to year, with average value -0.8%. For three years (1998, 1999, 2000) D was positive. Given the uncertainties, one cannot reject the hypothesis of zero gender bias: for 8 of the 11 years, D=0 was within the 1-σ error bars (68% confidence interval). Since there could conceivably be gender bias associated with the promotion process, it is possible that model 4 may underestimate the gender bias. On the other hand, model 3 where only departmental affiliation and time since PhD are considered in addition to gender will probably overestimate the gender bias. It is therefore reasonable to consider that the actual gender bias in salary falls somewhere between the results of model 3 and model 4. Thus, averaged over the 11-year period, the gender bias would appear to be between -3.6% and -0.8% for all Princeton faculty. Gender bias in salaries may be present, but it does not exceed about 3%, when averaged over the entire faculty. To focus on women in science and engineering, the above analysis has been carried out for only the faculty in Natural Sciences and Engineering, with results shown in Figure 2. The gender coefficients, averaged over the 11-year interval, are -2.3% for model 3 and -0.3% for model 4. The error bars are somewhat larger, due to the reduction in sample size. Appendix B: Section 3 Compensation Analysis 23

4 Figure 2. Gender differences in salary (as a percentage) for Natural Sciences and Engineering only. The same four models are applied. Averaged over the 11-year period, the gender bias for Natural Sciences and Engineering does not exceed about -2.3%, but model 3 falls to -4% in 2001/2 and 2002/3. To look for possible differences among the different areas of science, or between science and engineering, the above analysis was repeated on the following 4 subsets of the data: A. All Natural Sciences (Division III). B. Life Sciences: Molecular Biology, Ecology and Evolutionary Biology, and Psychology. C. Physical Sciences: Mathematics, Physics, Chemistry, Geosciences, and Astrophysics. D. Engineering (Div. IV): Civil & Environmental. Eng., Computer Science, Chemical Eng., Electrical Eng., Mechanical and Aerospace Eng., and Operations Research and Financial Eng. For each of these four samples, models 3 and 4 have been fitted to the data, resulting in lower and upper bounds on the gender bias in salary. Figure 3 shows the resulting gender coefficients Appendix B: Section 3 Compensation Analysis 24

5 for these 4 subsets. Because of the reduced sample sizes, the 1-σ uncertainties are increased relative to those in Figure 2. Table 1: Gender Bias in Salary, Average for (Negative entries indicate lower salaries for women.) Departmental Groupings Model 3 Model 4 Natural Sciences + Engr -2.3% -0.3% Natural Sciences -3.2% -1.7% Physical Sciences -3.5% -2.9% Life Sciences -4.3% -2.1% Div. IV: Engineering -5.1% -2.1% For all of Natural Sciences (see Table 1), the gender difference has a mean of -1.7% over the 11-year period if rank is allowed for (model 4). If no allowance is made for rank (model 3), the difference is -3.2%. However, for any given year the 1-σ uncertainty interval is approximately ± 4.5% so the bias is not statistically significant in any single year. This is apparent from the fact that zero falls within the 1-σ error bars for 8 of the 11 years (see Figure 3). To examine the possibility that there might be significant differences between different departments, the division of Natural Sciences has been divided into two subsets: (1) Physical Sciences and (2) Life Sciences. Physical Sciences has a gender difference of about -3% averaged over the 11 years, and similarly for Life Sciences. There is no evidence for significant differences between the physical science departments and the life science departments as regards gender bias in salary. Despite the 11-year history indicating that gender bias in salary does not exceed about 3%, it is disconcerting to observe a downward glitch in Figure 2 for 2001 and This is seen separately in Life Sciences and Physical Sciences (see Figure 3), so it is not the result of a single event: Physical Sciences had a gender difference (for model 4) of about -7% for years 2001 and Life Sciences had a gender difference (for model 4) of about -8% in 2001, and -5% in These downward glitches may be the result of retention and recruitment of individual senior men, or loss of senior women to other positions. Nevertheless, the hint of a trend is worrisome, particularly in view of the relative stability during the 9 preceding years. This trend should not be permitted to persist. Appendix B: Section 3 Compensation Analysis 25

6 Figure 3. Gender differences in salary (as a percentage) for four subsets of data: Engineering, all Natural Sciences, Physical Sciences and Life Sciences. Upper panels show gender differences for Engineering and for Natural Sciences. Lower panels show results for Physical Sciences (Mathematics, Physics, Chemistry, Geosciences, Astrophysics) and Life Sciences (Molecular Biology, Ecology and Evolutionary Biology, Psychology). For Engineering (see Figure 3), the gender difference (for model 4) has a mean of -2.1% over the 11-year period; 11 of the 11 years have D=0 within the 68% confidence interval. Appendix B: Section 3 Compensation Analysis 26

7 The conclusions of this analysis are as follows: over the 11 year period, Princeton University's salary policies appear to be close to gender-neutral (within 2-3%). However, for AY 2001/2 and AY 2002/3 the Natural Sciences show a gender difference of -6%, which must not be allowed to persist. 2. RECOMMENDATIONS The University should have as a target zero gender difference in salary to within ± 2% in each division, after allowing for years since PhD, department, and rank. The apparent downward trend in female salaries relative to male in Natural Sciences during AY 2001/2 and 2002/3 is disturbing. The Dean of Faculty's office should understand the causes of this downward trend, to ensure that it is not continued. The compensation analysis should be updated annually. This should be done in time to be available to the Faculty Committee on Appointments and Advancements (C/3) prior to setting salaries for the coming year. It might also be helpful to C/3 if software were available to the Dean of Faculty's office which would allow them to repeat the compensation analysis using the proposed salary increases, to see what the effects of proposed salary increases would be prior to making final decisions. Appendix B: Section 3 Compensation Analysis 27

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