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Published equation contexts

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

Why this formula appears here

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

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

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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