3.4
Interpretation
For readers unfamiliar with some of the notation and graphics included in this report, we provide below some brief explanations to facilitate understanding.
First, many findings are accompanied by “P-values.” In most cases these reflect the probability of observing positive regression coefficients at least as large (or negative regression coefficients as small) as those estimated in the analyses when, in reality, the coefficient equals zero. That is, when a variable has no association with the outcome in the analyses (the “null hypothesis”), the coefficient is expected to be close to zero. A positive association is reflected by a positive coefficient, and the converse holds for negative coefficients. The smaller the P-value, the less compatible the data are with the null hypothesis. Three levels of statistical significance (which reflect judgments about how compatible the evidence is with the null hypothesis) are reported: weakly significant (P<0.10), significant (P <0.05), and strongly significant (P < 0.01). The use of ‘weakly’ and ‘strongly’ are used to provide subjective interpretation to relative significance levels, and are not qualitative judgements about the direction or magnitude of di↵erences or e↵ects. The smaller the P-value, the more likely one would be to abandon the null hypothesis in favor of an alternate one favoring the presence of an actual association.
Two forms of regression analyses are included in this report. The more common one, linear regression, is used to model the relationship between a continuous outcome (such as the logarithmic transform of salary) and one or more predictor variables, which may be continuous or semi-continuous (e.g., rank/step interval), ordinal (e.g., decade of hire), or nominal (e.g., gender or ethnicity). The strength of the linear relationship between the pre- dictor variables and the outcome variable is measured by the correlation coefficient (r): a positive r indicates a positive relationship between the linear predictors and the outcome, and a negative r indicates a negative relationship. In this report correlation coefficients are used to show the relationship between academic progress (where 1 = normative progress;
< 1 = delayed progress, and > 1 = accelerated progress) and o↵-scale salaries in dollars. If data were perfectly correlated, all points in a scatterplot would lie on a straight line; if the slope of the line was positive, the correlation coefficient would be 1.0, and the con- verse would also be true. Correlation coefficients are accompanied by P-values. The null hypothesis of no association between predictor variables and the outcome corresponds to a correlation coefficient of zero. The smaller the P-value, the less likely it is that the true correlation coefficient is actually zero. For additional detail about correlation coefficients, see: Interpreting results: Correlation.
Not all outcomes in this analysis are continuous, though. We also address how factors potentially a↵ect the step of hire for Assistant, Associate, and full Professors. This outcome is ordinal, rather than continuous, so an alternate form of regression called ordered (ordinal) logistic regression was used. The null hypothesis of no association is similar to the one above (meaning the coefficients are expected to be close to zero), and the P-values have the same interpretation as with linear regression.
In this report we chose not to attempt to provide literal interpretations to each of the regression coefficients given the logarithmic transformations used. Instead, associations are described with respect to their level of significance (or non-significance), as well as their
3.4. Interpretation
direction (positive or negative).
For a particular rank, step, and SCU, variability in total salary can usually be attributed to the o↵-scale component. Scatterplots of current o↵-scale salaries for the entire university (except faculty on the Health Sciences Compensation Plan) and in each of the units are provided to demonstrate their relationship to academic progress. The plots contain three horizontal lines corresponding to the 25th, 50th, and 75th percentiles of o↵-scale salaries among faculty in the units actually receiving them (i.e., o↵-scale salaries of zero were not included in these calculations). The vertical line corresponds to a progress rate of 1.0, which is normative. Some random “noise” was added to each point in the scatterplot to reduce the number of points that are superimposed. Faculty whose points fall in the lower right quadrant are the most disadvantaged by virtue of their normative or accelerated progress, but comparatively low (or no) o↵-scale salary.
In addition, boxplots are presented to show the distribution of progress rates among fac- ulty receiving any current o↵-scale salary versus those receiving none. A horizontal boxplot is comprised of several parts. The “left edge” of the box corresponds to the 25th percentile of academic progress values; the “right edge” of the box corresponds to the 75th percentile of academic progress values; the vertical line inside the box corresponds to the 50th per- centile of academic progress values. The boxes typically have horizontal lines emanating from the bottom and top of them; these represent the distribution of most of the remaining progress values below the 25th and above the 75th percentiles. Outlying observations, which usually (but not always) are in the (approximate) lowest and highest 5th percentiles, are illustrated with individual points (although note that identical progress values have super- imposed points). A short video on the interpretation of boxplots provides additional detail: Boxplot Basics and Interpretation.
A final note: all statistical models are approximation of unknown, underlying relation- ships between variables. They represent, in a sense, a combination of our own belief struc- tures and the evidence that the data provide. Thus, models contain implicit assumptions that may or may not be correct and represent approximations to the truth. For example, the functional relationship between year of hire and current salary is likely to be complicated, non-linear, and challenging to individually model for each unit. Conversely, modeling each year of hire separately would obviate us of the need to functionally describe an e↵ect, but doing so could compromise model precision and validity, particularly in small units, because of the need to estimate so many regression coefficients. So we elected to analyze our findings using decade of hire, the e↵ects of which are assumed to be constant within the decade and that change in a step-wise fashion at the boundaries of the decade. All models are, to some extent, wrong (misspecified), for not only the above reasons, but also because we can never know precisely every factor that influences a faculty member’s salary, especially the negotiated component.
Data
All data used in this report were collected and provided to the Task Force by the Office of the Vice Provost - Academic A↵airs. The report’s main dataset was primarily based on the data in the Payroll Personnel System Data Warehouse on October 1st, 2014, focusing only on Ladder Rank Faculty. A second dataset was provided by the School of Medicine that also included Professors of Clinical , and Health Sciences Clinical Professors. Of the 1,505 faculty employed as of October 1, 2014, 16 were excluded from the analysis due to missing data and/or being hired before 1975.
4.1
Variables: Office of the Vice Provost-Academic Af-
fairs dataset
• Composition — Ladder Rank faculty, does not include the Chancellor, the Provost, Vice Chancellors, Vice Provosts, Deans, and the academic series Supervisor of Physical Education.
• Salary — Regular Ladder Rank faculty salary. For the Schools of Medicine all salary sources have been included. For the Graduate School of Management and the School of Law summer compensation provided by the respective Dean’s office has been included. Salary does not include stipends, compensation from external funding sources (includ- ing summer compensation), and summer compensation connected with administrative duties.
• Normalization of Starting Salary — in order to compare starting salaries for current employees, these were converted to real dollars using the Consumer Price Index for All Urban Consumers (Bureau of Labor Statistics 2014). To reflect current conditions, salaries were converted using 2013 as the base year.
• Employee ID (names are not included)
• Gender (male or female)
• Ethnicity — based on Department of Labor guidelines, combining faculty into the groups Asian, Black, Hispanic, Native American, Caucasian, and Unknown. The dataset also includes an indicator for traditionally Underrepresented Minorities (URM) which combines the categories Black, Hispanic, and Native American.
4.1. Variables: Office of the Vice Provost-Academic A↵airs dataset
• Starting O↵-scale Salary — O↵-scale salary at the time the person started as a Ladder Rank faculty member.
• Years Since Start — number of years since the person started as a Ladder Rank faculty member.
• Start After Degree — number of years since earning the degree recorded for “Education Level and Year”.
• Beginning Rank and Step (Interval) — the academic rank (Assistant, Associate, or full) and the step the person was at when hired. Rank and step has also been translated into an interval in order to account for overlapping steps between the academic ranks.
• Years Above/Below Since Last Action — the number of years a person is above or below what would be expected to be normal progress. The calculation:
Normative Progress + Stop the Clock or Work/Life Deferral - Actual Time Taken Normative Progress — the number of years a person would take at normal time to
advance from their beginning rank/step to their current rank step.
Example: A person starts at Associate Professor Step 3, receives a merit to Associate Professor Step 4; this normally takes 2 years, receives a merit to full Professor Step 2; this normally takes 3 years. Normal Progress for this merit and promotion would be 5 years.
“Stop the Clock” or Work/Life Deferral — for each time the program was used one additional year is added to normative progress.
Actual Time Taken — the number of years that have elapsed between a person’s start date and the person’s last action. Last action includes denied actions, deferrals, and five year reviews.
Example: if a person starts at Associate Professor Step 3 and advances to full Pro- fessor Step 2 in four years, then their “Years Above/Below Since Last Action” would be 5 + 0 - 4 = 1, or one year above normal progress.
• Current Rank and Step (Interval) — the academic rank (Assistant, Associate, or full) and the step the person is at. The rank and step has also been translated into an interval variable in order to account for overlapping steps between the academic ranks.
• Department and Unit (School, College, or Division) — each person is assigned to a primary department and college.
• Primary Academic Salary Scale — identifies the salary scale each person is on; when a person is on more than one scale the higher salary scale is used. The salary scales are:
Professor, Academic Year Professor, Fiscal Year