subscript

The passage around this formula

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 $\bar{Y}_n - \bar{Y}_N = \rho_{R,Y}\sqrt{\frac{1-f}{f}}\,\sigma_Y$. where $\rho_{R,Y}$ is the “data defect correlation” between selection and outcome…

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