Two weeks ago, The Daily Pennsylvanian highlighted a claim in a recent Senate Committee report that there is a gender wage gap at Penn. This “2-3 percent” gap — favoring male professors with extra pay for apparently equal work — was underscored as gravely concerning due to its “compounding effect ... over a faculty member’s career.”
I began investigating this startling allegation on the assumption that a reporter had misrepresented the mathematical statements of the Senate Committee. To my surprise, I found instead that the Senate Committee had constructed a “distressing” “gender bias in salary” at Penn by making two numerically illiterate arguments, one muddled and the other — as written — plainly false.
Naturally, I doubted myself — and tried to contact the Office of the Faculty Senate with no response. But after consulting with friends and getting second and third opinions from professors, I concluded that the report did, indeed, assert an impactful gender wage gap at Penn without data-driven support.
The report draws on two separate studies of earnings by gender at Penn — one conducted externally and the other by the Senate Committee itself. The external analysis, after correcting for field, rank and time in rank, found a gender earnings gap of “less than 2 percent.”
Accordingly, the Committee did not use the external analysis to claim a gender wage bias at Penn. Instead, it underscored its own finding of a “2-3 percent” earnings gap, adjusted for field and rank. But the Senate Committee explicitly states that this gap was “not statistically significant on an annual basis.” Nor could they claim it was statistically significant on any other basis — for their analysis did not incorporate data from previous years.
Statistically insignificant results, as professor Abraham Wyner of the Statistics Department explained, indicate that the test applied to find a difference between male and female wages failed to prove any probable disparity between the two. That is, the 2-3 percent wage gap in the particular sample of professors studied might have been the result of random chance. A different sampling of similarly situated Penn professors — in a different fiscal year, for instance — might produce no gap at all, or even show men earning, on average, less than women.
Thus, the Committee’s assumption that their statistically insignificant results represent systematic “gender bias in salary” is unsubstantiated at best.
But the report builds upon this assumption an even more incredible claim.
Apparently conscious that a 2-3 percent wage gap — if statistically significant — still might seem unalarming, the Committee states that “an annual 2 percent difference in salaries would result in 22 percent more total earnings for a typical male faculty member over 10 years than a typical female faculty member, and a gap of 48 percent more total earnings over 20 years.”
As Wyner explains, in order for the gap to compound over time as the Committee assumes, the percent difference between male and female salaries could not remain constant at 2 percent every year. Instead, men would have to enjoy 2 percent higher raises annually. “So, if men were getting — say — 4 percent raises, women would have to be getting less than 2 percent raises.” But the report specifically investigated the possibility of difference in “annual salary increases” and found a “general parity” — both male and female professors receiving approximately 3 percent raises every year.
This leaves no room for reinterpreting the reports’ absurd assertion that a constant 2 percent annual difference in salaries would result in “48 percent more total earnings over 20 years” for men. And even a high schooler can calculate that if Jill earns exactly 98 percent of Jack’s salary every year, the difference in total earnings between Jack and Jill will remain at exactly 2 percent, no matter how many years may pass.
Thus, the “gender bias in salary” of “2-3 percent” at Penn — purported to have enormous significance on a typical female professor’s total earnings — turns out to be quite possibly nonexistent and, even if we brashly assume it does exist, an inconsequential percentage of total earnings over a career.
How did a panel of professors at Penn make such simple mistakes smack in the middle of a sophisticated examination of salaries at one of the most progressive institutions in America?
It is hard to say. But the error made Wyner recall Richard Feynman’s first principle of science: You must not fool yourself, for you are the easiest person to fool. It is just possible that someone wanted so badly to find consequential gender wage bias at Penn that they fooled themselves into discovering the result they were looking for.
JEREMIAH KEENAN is a College senior from China, studying mathematics and classical studies. His email address is firstname.lastname@example.org. “Keen on the Truth” usually appears every other Thursday.Comments powered by Disqus
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