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Equation 20 · Part 9 · Forty Million Clicks Through One Uneven Door

Denominator: 1-f_c

CSDBc(δ)=δσYfc1−fc.\mathrm{CSDB}_c(\delta) = \frac{\delta}{\sigma_Y}\sqrt{\frac{f_c}{1-f_c}} .
1−fc1-f_c

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

1-fcf_c occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

Solving for the minimum defect correlation needed to produce a given bias δ\delta , and taking the most generous possible bound for a roughly binary preference indicator, σY\sigma_Y ≤\le 0.5 , gives what this article calls, for a specific country c , its Country Selection-Divergence Bound: CSDBc(δ)=δσYfc1−fc\mathrm{CSDB}_c(\delta) = \frac{\delta}{\sigma_Y}\sqrt{\frac{f_c}{1-f_c}} . This is a DERIVED quantity, not a measurement: it has not been run against real per-country population totals or the actual SharedResponsesSurvey.csv microdata, and no value of ρR,Y\rho_{R,Y} for any real country is claimed here. What can be computed honestly, using only the paper’s own reported extremes for n — 101 respondents at the low end, 448,125 at the high end [ 1 ] — is how small…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.