Mathematics and Education

A slow blog

The Garbled Statistics

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[Update: A revised version of this post appears as part of Rumors of Our Rarity are Greatly Exaggerated: Bad Statistics About Women in Science, Journal of Humanistic Mathematics, July, 2011.]

Like The Female Brain, “The Science of Sex Differences in Science and Mathematics,” published in Psychological Science in the Public Interest in 2007, discusses the idea that women, more than men, avoid careers in academic science. As I read it, I noticed statistics that seemed outdated—or just plain wrong. The cited source was old (1997) and unlikely—an article on intelligence rather than a survey. The statistics claimed to give percentages of tenure-track women in science at “elite” universities. In particular, women were supposedly 8.3% of tenure-track faculty at “elite” mathematics departments.

Of course, the 8.3% could have been correct, depending what “elite” meant. After all, I knew of one elite mathematics department that hadn’t hired any tenure-track women during a ten-year period. With the right choice of departments, one could probably produce 8.3%. However, a 2002 survey[i] listed in the bibliography and cited near the statistics seemed like a good candidate for the source—and, in fact, the numbers suggest that it was.

The Psychological Science numbers matched those from the survey, but the categories didn’t. In the survey, these numbers indicated the percentages of women in all positions at the top 50 departments—not the percentages of women in tenure-track positions as stated in the Psychological Science article. As do many surveys of faculty demographics, this survey found a substantial difference between the percentages of women who were assistant professors and in all ranks. In mathematics, women were 8.3% of all ranks: 19.6% of assistant professors, 13.7% of associate professors, and 4.6% of full professors.

In 2007, the survey of the top 50 science departments was repeated.[ii] As occurs often in surveys of science faculty demographics, the percentages of women in most categories had increased. In mathematics, women were 28% of assistant professors at the “top 50” departments rather than 19% that they were five years earlier.

**Top 40 departments

In 2008, a magazine called The American published an article about women in science called “Why Can’t a Woman be More like a Man?” It said:

Women comprise just 19 percent of tenure-track professors in math, 11 percent in physics, 10 percent in computer science, and 10 percent in electrical engineering.

This time I couldn’t guess the source of the numbers—but readers of this article will. These numbers were not only rounded in an unusual way and relabeled (“assistant professor” rather than “tenure track”), but out of date.

Most importantly, this information was not identified as pertaining to the “top 50 departments” or even “elite” departments. It appeared to refer to departments at all colleges and universities. There is no reason to assume that the situation for elite universities is the same as that for all academic institutions. In many surveys of faculty demographics, the percentage of female tenured or tenure-track faculty is inversely proportional to the prestige of the institution. For example, in mathematics, the 2005 Conference Board of the Mathematical Sciences Survey found women were 33% of tenure-track professors in MA-granting departments, but 28% of those in PhD-granting departments. (See AAUP surveys for other examples.) So, I was quite puzzled to see The American’s figures which seemed to say that women were, on average, 19% of tenure-track faculty in all mathematics departments—elite and otherwise.

I contacted the editor of The American. The author sent me the source, an article in Science which gave—correctly—the findings of the 2002 survey.[iii] I replied, mentioning the 2007 survey and recent results for mathematics. The American did not post an update or correction. (However, the author, Christina Hoff Sommers, used the 2007 numbers for assistant professors in her essay for The Science on Women and Science, but again neglected to mention that these referred to assistant professors at the “top 50” universities, not universities in general.)

Harder to kill than a vampire—the two sets of published “statistics” on the percentage of female tenure-track professors in science and engineering remain on the Web.

But, surely no one would use those. Not only were they obviously wrong (at least to the cognoscenti), but readers might easily guess that they came from secondary sources and look for the primary sources.

Imagine my surprise, when I read in August of 2009:

Nearly half of all physicians and biologists are females, as are the majority of new psychologists, veterinarians, and dentists, suggesting that women have achieved equality with men in the workforce. But the ranks of professionals in math-intensive careers remain lopsidedly male; up to 93% of tenure-track academic positions in some of the most mathematically-oriented fields are held by men.

Thus begins the advertising copy for a new book called The Mathematics of Sex. Where does the 93% come from? I have not found a reference for it in the book, but I think that I can guess its origins.

In 2008, one of the authors of The Mathematics of Sex gave a talk at the Templeton Foundation. His slides, once posted here, give the garbled Psychological Science statistics, followed 55 slides later by those from The American.

The smallest percentage in the Psychological Science list is 7% when rounded. Subtract the 7% from 100%. Drop the “elite” and you get 93% of tenure-track professors in some subfields of engineering are men.

But, some readers will be screaming, even if the statistics were correct, you can’t drop the “elite”! Doesn’t everyone in academe know that statistics about elite universities do not necessarily describe all universities? (Does anyone think the average university has an endowment the size of Harvard’s? Does anyone think the average university has salaries like Princeton’s?) Doesn’t everyone in academe know that without other modifiers “tenure-track positions” is likely to be interpreted as referring to academic institutions in general?

Apparently someone involved in the production of the book did not think of these things. Maybe it was a research assistant, or an author, or a copy editor—or some unhappy concatenation of the three.

I arrived at this conjecture, after much puzzlement, with the aid of Joel Best’s books on statistics.[iv] In any event, two rather different groups of “statistics” about tenure track positions in science have been published in 2009.

According to page ix of The Mathematics of Sex,

Anywhere from 64% to 93% of the professors on tenure track in these [mathematically intensive] fields are men.

According to page 80 of The Science on Women and Science,

Women comprise just 28 percent of tenure-track professors in math, 18 percent in physics, 20 percent in computer science, and 14 percent in electrical engineering.


[i] D. Nelson, & D. Rogers, A National Analysis of Diversity in Science and Engineering Faculties at Research Universities, 2004.

[ii] D. J. Nelson, C. N. Brammer, & H. Rhoads. A National Analysis of Minorities in Science and Engineering Faculties at Research Universities. Diversity in Science Association and University of Oklahoma, Norman, OK. October 31, 2007.

[iii] J. Handelsman et al., “More Women in Science,” Science, 309, no. 5738 (2005): 1190–1191.

[iv] J. Best, Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists, University of California Press, 2001; J. Best, Stat-spotting, University of California Press, 2008.


Written by CK

March 9, 2010 at 4:43 pm

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