Chess psychometrics – The gender equality paradox

Chess databases contain millions of games, whose players can largely be identified by the Fide players database [1] which contains age, sex, nationality and ratings. These games are interactions providing information about behavior in a competitive context. They are a goldmine for psychological or sociological research into a wide range of topics. The datasets derivable from chess databases are much larger than what can be realistically achieved in typical psychological research. As a researcher you are really only limited by your imagination and the number of your grad students.

While the typical university professor is severely limited in the former, I am unfortunately limited in the later. So, we will see how many of my chess psychometrics projects I’ll be able to bring to completion. For now we’ll start with something simple and not very original: We will check whether the gender equality paradox holds in chess.

The gender equality paradox is the observation that women in more gender equal societies tend to choose more stereotypical female occupations and are less likely for example to go into STEM. The gender disbalance in chess is very comparable to the disbalance in STEM research [2]. In fact, it is usually even more extreme, with women in many countries only representing less than 5% of the pool of rated players.

Outside of developed countries, the number of rated players is often quite small and not very representative when it comes to age, rating or possibly sex. So it is not surprising that on a global level we find no correlation between the global gender gap index and the fraction of female players.

In European countries however, there is a significant negative correlation between gender equality and the fraction of female players. (Yes, Turkey is for some reason in my list of European countries.)

Pearson correlation: -0.43603692297301305, p-value: 0.01119225533794084

This looks like a straightforward result. However, I am generally skeptical about the significance of these kind of correlations, because I suspect that often the significance is a result of countries falling into a small number of similar behaving clusters. If these clusters are then arranged linearly by chance, we get a significant correlation by virtue of decomposing these clusters into many countries.

So it might be the case that Northern countries all have high gender equality and low female chess player fractions by chance. While Eastern Europeans have low gender equality and high female chess participation for historical reasons. Because these clusters and the rest of the countries in between constitute a lot of observations the results looks a lot more robust than it really is.

Sure enough, there is no such correlation in Eastern Europe and restricted to Western Europe the correlation looses all significance.

On the other hand, the loss of statistical significance is due to just two outliers: Iceland and France. So is the gender equality paradox a thing in chess or not?

To detect even a rather weak tendency, we average over all countries that fall into the same section of the GGG-index. This time we look at all countries in our dataset.

If we ignore the four countries with the lowest gender equality which average very low, we actually see a nice downward trend in female chess playing the higher the gender equality. I tentatively conclude that the gender equality paradox does actually exist in chess.

[1] Fide player database
https://ratings.fide.com/download.phtml

[2] The Gender-Equality Paradox in STEM Education
https://journals.sagepub.com/doi/abs/10.1177/0956797617741719?journalCode=pssa

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