Are University Admissions Biased? | Simpson’s Paradox Part 2

Are University Admissions Biased? | Simpson’s Paradox Part 2

October 16, 2019 0 By Stanley Isaacs


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