Data on abilities reveal a great deal of overlap for men and women
In 2005 Lawrence Summers, then the president of Harvard, caused an uproar by appearing to suggest that the lack of women professors in math and science might arise from biological differences. Fifteen years on, a gender imbalance in these fields persists and the arguments rage on. I believe math can help us to progress.
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The discipline of math involves, among
other things, ironing out ambiguities and providing clear definitions for
comparisons. Men and women are not homogenous groups of people who all behave
in the same way, so we need ways to understand whole sets of data.
Averages are one well-known way; we can
compare how men and women do at something “on average.” There are different
types of averages: The mean is where we add up all results and divide by the
total number of people, and the median is the 50th percentile that tells us
that half the people rank above it and half rank below. For example, the mean
height of men in the
That spread of data can be studied via
the standard deviation, which is calculated from the distance that each data
point ranges from the mean. For a standard bell curve, a distance of “one
standard deviation” on either side of the mean always comprises a fixed
proportion of the results, around 70%.
Average marathon times for men and
women differ by about 30 minutes. That sounds like a lot, but the fastest women
run marathons twice as fast as the average men.
The standard deviation for height is
around 2.5 inches, so the mean heights of men and women are about two standard
deviations apart. Thus, around 95% of women are shorter than the average for
men, but there is still a noticeable overlap. For data sets that differ by one
standard deviation or less, there is more substantial overlap.
Average marathon times for men and
women differ by about 30 minutes, for instance. That sounds like a lot, but is
only half the standard deviation of one hour—and the fastest women run marathons
twice as fast as average men.
Height and running times are
particularly easy to measure, but men and women have also been compared in
broader areas of behavior, such as mathematical skills, aggression and
self-esteem.
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In 2005, Jane Shibley Hyde collated a
large collection of meta-analyses of these differences. In her book “Inferior,”
Angela Saini sums up the results: “In every case, except for throwing distance
and vertical jumping, females are less than one standard deviation apart from
males. On many measures, they are less than a tenth of a standard deviation
apart, which is indistinguishable in everyday life.” For example, “mathematics
problem solving” was found to be better in men by just 0.08 standard
deviations; interestingly, women were found to out-perform men at “mathematics
concepts” by 0.03 standard deviations. Men showed more self-esteem by a range
of 0.04 to 0.21 standard deviations, increasing through adolescence; they were
found more likely to make “intrusive interruptions” by 0.33 standard
deviations.
The differences may be interesting, but
they are also very small. The differences within each gender are greater than
the differences between genders, so gender is not a good predictor of these
behaviors.
Such comparisons are blurred, of
course, by issues beyond the reach of mathematics. Many of the behaviors studied
are much harder to define and measure than height or marathon times and involve
some mix of biological and sociological influences. But it is logically flawed
to infer a biological difference from a statistical difference. Mathematics
provides us with powerful tools, but we have to know their uses and
limits.
—Dr. Cheng’s new book, “X+Y: A
Mathematician’s Manifesto for Rethinking Gender,” will be published Aug. 25 by
Basic Books.
https://www.wsj.com/articles/what-the-numbers-say-about-gender-differences-11596752225
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EVERYDAY MATH
Data on abilities reveal a great deal of overlap for men and women
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