Mathematics and Education

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Archive for the ‘quantitative literacy’ Category

The Tyranny of the Mean

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In the appendix footnote 3 of a forthcoming 2015 article, Ceci and Williams state:

Many commentators have opined that female scientists are superior to their male counterparts, and therefore the fact that they are hired at the same rate as men obscures the fact that they should be hired at even higher rates, if merit was the basis for hiring.

Ceci and Williams give three quotes intended as examples of this argument. One comes from my blog post The Pipeline and The Trough. However, as I stated in a later post, I did not give this argument.

So why do Ceci and Williams think I did? The answer may lie in “the tyranny of the mean”—the assumption that the mean for a set, e.g., “female scientists,” is the same as the mean of a subset, e.g., “female applicants for a given job.” Read the rest of this entry »


Written by CK

October 19, 2015 at 4:22 pm

A Female Advantage in Academic Hiring?

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In their recent Proceedings of the National Academy of Sciences article about tenure-track hires, Williams and Ceci say:

A number of audits of hiring by universities have been reported in the past two decades and these have reported either a neutral playing field in non-mathematical fields . . . , or, more commonly, a pronounced female hiring advantage in math-intensive fields. . . . Here is what we know about the female advantage in real-world hiring of tenure-track applicants in STEM fields in the United States and Canada: There is a female advantage in all large-scale studies dating back to the 1980s. (SI Appendix, p. 26, emphasis added)

Williams and Ceci quantify “female preference” as the ratio of female hires to female applicants. However, they do not compute these ratios for the “audit studies” they cite. This post makes some of those computations.

Interestingly, three of the eight studies cited come from Canada, but some large-scale audit studies of United States universities are not mentioned. This post examines a few of the studies that could have been cited, finding that the claim above is not supported and offering an alternative explanation for the statistics in the US audit studies.

Update (August 2015): Ceci makes an assumption explicit (see comments section here and further discussion below).

Iqbal 2000 Fig 1Update (July 2015): The three Canadian studies concern hiring in the 1980s and 1990s. During this period, the gender distribution of Canadian faculty hires may have been affected by a “brain drain” to the United States. Studies note that PhDs were overrepresented among these migrants. What is known suggests that a very large proportion of these PhDs were male and among “the best and the brightest.” Thus, faculty hiring patterns in Canada and the United States may differ. Moreover, an exodus of men may be a factor in the apparent overrepresentation of women as hires in Canada. Further discussion is below.

Figure from Iqbal, M. (2000). Brain drain: Empirical evidence of emigration of Canadian professionals to the United States. Canadian Tax Journal, 48(3), 674–688.

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Written by CK

May 11, 2015 at 3:14 pm

Save the Phenomena!

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Last Halloween, the psychologists Wendy Williams and Stephen Ceci wrote an op-ed in New York Times claiming that “academic science isn’t sexist.” Among other things, they suggest that bias doesn’t occur in hiring, writing of “alleged” hiring bias. In a longer article, Ceci and three co-authors claim that “the evidence in support of biased hiring as a cause of under-representation is not well supported, and even points in the opposite direction.” The same evidence is interpreted as a “female hiring advantage” in Williams and Ceci’s “2:1 Faculty Preference for Women on STEM Tenure Track.”

I think the reason why this evidence “points in the opposite direction” is that Ceci et al. do not “save the phenomena” by accounting for crucial details of the findings they cite. Thus, these findings may not be consistent with the findings of Williams and Ceci’s experimental study. This raises concerns about the ecologically validity of the experimental study, e.g., that it may be not realistic to assume that a strong female applicant will often be described as “creative” or “a powerhouse.”

Here are details. Read the rest of this entry »

Written by CK

April 14, 2015 at 4:33 pm

Understanding Underrepresentation

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. . . is the title of my article in the Mathematical Intelligencer on the distribution of women in mathematics and other fields. I’ve posted the manuscript version here. Read the rest of this entry »

Written by CK

January 11, 2014 at 11:11 am

“Underrepresentation of Women in Math-intensive Fields”?

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Some characterize the situation for women in STEM as “underrepresentation of women in mathematically-intensive fields.” In the case of baccalaureates at least, the situation might be more accurately described in terms of salaries—unless you believe that engineering and computer science are more “mathematically-intensive” than mathematics. Read the rest of this entry »

Written by CK

November 10, 2012 at 11:49 am

The Pipeline and the Trough

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In the U.S., women currently get about 29% of PhDs in mathematics. But, in PhD-granting mathematics departments only 13% of the faculty members are women.

Does this mean that women are dropping out between PhD and first job? No!

Does this mean that women are not getting hired in proportion to their share of PhDs? No!

The evidence is discussed in this article, called “The Pipeline and the Trough.”

The 29% and 13% are examples of what I call (respectively) “pipeline” and “trough” statistics. Relative to the “PhD pipeline,” a collection of tenured and tenure-track positions (e.g., positions in a math department) is like a trough. Periodically, the PhD pipeline feeds a few new PhDs into the trough, and periodically a few faculty members leak out, due to death or retirement. In general, the composition of the trough is slow to change. Read the rest of this entry »

Written by CK

February 15, 2012 at 9:55 pm

Half of Women Do Not Have “Female Brains”

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. . . and half of men do not have “male brains,” according to research of Simon Baron-Cohen and his colleagues. See Table 1 of Goldenfeld, Baron-Cohen, & Wheelwright, 2005, Empathizing and systemizing in males, females and autism, Clinical Neuropsychiatry, 2, 338–345. More details are below.

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Written by CK

December 15, 2011 at 10:52 am