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Published equation contexts

f=n/Nf = n/N

Why this formula appears here

where ρR,Y\rho_{R,Y} is the “data defect correlation” between selection and outcome across the full population, f = n/N is the sampling fraction, and σY\sigma_Y is the outcome’s population standard deviation. The identity’s uncomfortable lesson for any self-selected big-data project is that the error term does not shrink as n grows unless f grows with it — and for a national population sampled through a viral website, f stays vanishingly small no matter how large n gets. Meng introduced this identity using the 2016 US presidential election’s Cooperative Congressional Election Study data as its worked example, and the pattern he documents there is the same “Law of Large Populations” this article is…

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f=n/Nf = n/N

Equation 11 · AI Ethics

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

where ρR,Y\rho_{R,Y} is the “data defect correlation” between selection and outcome across the full population, f = n/N is the sampling fraction, and σY\sigma_Y is the outcome’s population standard deviation. The identity’s uncomfortable lesson for any self-selected big-data project is that the error term does not shrink as n grows unless f grows with it — and for a national population sampled through a viral website, f stays vanishingly small no matter how large n gets. Meng introduced this identity using the 2016 US presidential election’s Cooperative Congressional Election Study data as its worked example, and the pattern he documents there is the same “Law of Large Populations” this article is…

Meanings in this article

  • NN: the sampling fraction.
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