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Many chess players believe that women play worse chess than men. Here is how to respond.
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Their argument is typically a variant of "the best male player is much higher rated than the best female player". This was also the argument in a recent article on the Indian website @livemint, "Why women lose at chess" ( https://www.livemint.com/mint-lounge/features/why-women-lose-at-chess-11601626319872.html)
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But... the proportion of rated female players is very low (most likely due to many systemic disadvantages and biases that they face).
If you want to compare groups of unequal sizes, it's a really bad idea to use the top individuals as a metric.
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If you want to compare groups of unequal sizes, it's a really bad idea to use the top individuals as a metric.
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Let’s say group A has 10 people, group B has 2. Each of the 12 people randomly gets assigned a number between 1 and 100. Then I use the highest number in Group A as the score for Group A and the highest number in Group B as the score for Group B.
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On average, Group A will score 91.4 and Group B 67.2. The only difference between Groups A and B is the number of people. The larger group has more shots at a high score, so will on average get a higher score.
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In this article on @ChessBase, I show that on average, Indian women play as well as men, and that the gap between the top female and the top male Indian player can easily be due to the participation gap only.
https://en.chessbase.com/post/what-gender-gap-in-chess
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https://en.chessbase.com/post/what-gender-gap-in-chess
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Essentially the same argument was made back in 2009 by Merim Bilalić, Kieran Smallbone, Peter McLeod, and @FernandGobet, but chess players don't know this article or choose to ignore it.
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If you take into account how chauvinist and actively oppressive the chess world is towards women (see also this: https://en.chessbase.com/post/women-in-chess-role-of-innate-ability-beliefs), it's safe to say that the top female chess players are actually OVERperforming.
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Anyway.. next time someone tells you that women are inferior to men because @MagnusCarlsen is much higher rated than Hou Yifan, tell them to do a permutation test and then try again.
(Matlab code in the Chessbase article).
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(Matlab code in the Chessbase article).
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