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They also say that if they do the analysis globally the effect goes away. Curious, does that not imply that if one domain is biased against some group there would be another where the bias was in its favor?

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Also has issues of random chance causing these differences. How many different positions are there that have the chance of a 80% effect?

They're using a Benjamini–Hochberg correction (alpha=0.05) to account for multiple comparisons (see Table 2).

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