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.
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