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Equation 9 · Part 5 · Forty Million Clicks Through One Uneven Door

Symbol sigma_Y

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

What this part means

the outcome’s population standard deviation.

Its job in the formula

sigmaYa_Y is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

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 passage around this formula

…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 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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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