Symbol f

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…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 across the full population, f = n/N is the sampling fraction, and $\sigma_Y$ 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…

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