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Published equation contexts

Yˉn−YˉN=ρR,Y1−ff σY\bar{Y}_n - \bar{Y}_N = \rho_{R,Y}\sqrt{\frac{1-f}{f}}\,\sigma_Y

Why this formula appears here

A critique earns the right to be taken seriously only once it can say how large the effect it is worried about would need to be, and Xiao-Li Meng’s 2018 identity for bias in self-selected big-data samples gives a way to say exactly that, using only numbers the paper and its data-availability statement already make public [ 11 ] . For a population of size N with a binary response indicator R (did this person’s data reach the sample) and an outcome Y (their realized value on some Moral-Machine-relevant preference indicator), Meng’s identity relates the sample mean to the true population mean as Yˉn−YˉN=ρR,Y1−ff σY\bar{Y}_n - \bar{Y}_N = \rho_{R,Y}\sqrt{\frac{1-f}{f}}\,\sigma_Y . where ρR,Y\rho_{R,Y} is the “data defect correlation” between selection and outcome…

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Yˉn\bar{Y}_n

Symbol barY_n

barYnY_n is part of the quantity the equation computes from the expression on the right.

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YˉN\bar{Y}_N

Symbol barY_N

barYNY_N is part of the quantity the equation computes from the expression on the right.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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Yˉn−YˉN=ρR,Y1−ff σY,\bar{Y}_n - \bar{Y}_N = \rho_{R,Y}\sqrt{\frac{1-f}{f}}\,\sigma_Y ,

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

A critique earns the right to be taken seriously only once it can say how large the effect it is worried about would need to be, and Xiao-Li Meng’s 2018 identity for bias in self-selected big-data samples gives a way to say exactly that, using only numbers the paper and its data-availability statement already make public [ 11 ] . For a population of size N with a binary response indicator R (did this person’s data reach the sample) and an outcome Y (their realized value on some Moral-Machine-relevant preference indicator), Meng’s identity relates the sample mean to the true population mean as Yˉn−YˉN=ρR,Y1−ff σY\bar{Y}_n - \bar{Y}_N = \rho_{R,Y}\sqrt{\frac{1-f}{f}}\,\sigma_Y . where ρR,Y\rho_{R,Y} is the “data defect correlation” between selection and outcome…

Meanings in this article

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