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  • 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 applicantsif 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 were biased and even hint at where those biases are (or aren’t) coming into

  • play.

  • No, the paradox is that weve remained so reluctant to fight our biases, even when theyre

  • put in plain sight.

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Imagine a future cat-topia where both cats and people are applying to the physics and


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大學錄取有偏見嗎?| 辛普森的悖論第二部分 (Are University Admissions Biased? | Simpson's Paradox Part 2)

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    林宜悉 發佈於 2021 年 01 月 14 日