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Imagine a future cat-topia where both cats and people are applying to the physics and
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astronomy departments.
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In astronomy, 2 cats are accepted and 2 are rejected, while 1 human is accepted and 1
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is rejected.
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In physics 1 cat gets in and 2 don't, while 2 humans get in 4 don't.
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So, overall at the university, 3 cats are accepted and 4 rejected for a 43% acceptance
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rate, while 3 humans are accepted and 5 rejected for a 38% acceptance rate.
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Is the university discriminating against humans in its application process?
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Possibly not.
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That's because if each department reviews its own applications, then the numbers show
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that the astronomy department lets in 50% of cats and 50% of humans, which seems fair,
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and the physics department lets in 33% of cats and 33% of humans, which again seems
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fair.
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The reason, then, for the apparent unfairness at the university level is the imbalance in
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how many cats and humans apply to each department: more of the cats applied to the astronomy
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department, which happened to let in more applicants (regardless of species), while
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more of the humans applied to physics, which let in fewer applicants.
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This situation is another illustration of Simpson's statistical paradox, and something
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like it actually happened at Berkeley in the 1970s, which realized it was letting in 44%
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of men applying to the graduate school, but only 35% of women.
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Careful analysis was able to show that women tended to apply more to departments that had
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less funding and fewer places, like English, and men tended to apply more to less competitive
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departments, like engineering.
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Thus within each department (which was the level at which applications were evaluated),
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there wasn’t obvious evidence of gender discrimination among applicants – if anything,
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women were favored.
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And yet, the unequal distribution of women and men across departments resulted in an
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unequal distribution of women and men at the university overall.
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The question, then, is what caused the unequal distribution of women and men to begin with?
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One can of course imagine a sinister institution knowing how Simpson's paradox works, wanting
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to discriminate against a particular group, and thus advertising smaller, more competitive
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departments more heavily to that group, and vice-versa for groups they want to promote
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. More realistically, certain departments or fields may have reputations for being unwelcoming
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and unsupportive towards women even if they let them in fairly, and it’s also possible
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that aspects of a university itself attract applicants who are more likely to follow gendered
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career stereotypes.
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But ultimately, as the Berkeley study concluded, the problem is a bigger, societal, one: “Women
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are shunted towards fields of study that are generally more crowded, less productive of
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completed degrees, less well funded, and that frequently offer poorer professional employment
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prospects…
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The absence of a demonstrable bias in the admissions system does not give grounds for
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concluding that there must be no bias anywhere else in the educational
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process.”
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Those words were written in a statistics paper in 1975.
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And more recent statistics tell us that they still remain true today - which is unfortunate
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if you think women and men should have equal opportunities and/or be paid equally for equal
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work.
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So the paradox isn’t really in the statistics, since after careful analysis, the statistics
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tell us we’re biased and even hint at where those biases are (or aren’t) coming into
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play.
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No, the paradox is that we’ve remained so reluctant to fight our biases, even when they’re
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put in plain sight.
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This video is sponsored by Skillshare, the online learning site with courses on all sorts
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You can get two months free by going to skl.sh/MinutePhysics.
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Again, that’s skl.sh/MinutePhysics