fraction

The passage around this formula

Solving for the minimum defect correlation needed to produce a given bias $\delta$ , and taking the most generous possible bound for a roughly binary preference indicator, $\sigma_Y$ $\le$ 0.5 , gives what this article calls, for a specific country c , its Country Selection-Divergence Bound: $\mathrm{CSDB}_c(\delta) = \frac{\delta}{\sigma_Y}\sqrt{\frac{f_c}{1-f_c}}$. 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 $\rho_{R,Y}$ 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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