“Statistical Notes § Power Analysis for Racial Admixture Studies of Continuous Variables”, Gwern2014-07-17 (, , , , , , , , , , ; similar)⁠:

Miscellaneous statistical stuff

I consider power analysis of a genomic racial admixture study for detecting genetic group differences affecting a continuous trait such as IQ in US African-Americans, where ancestry is directly measured by genome sequencing and the comparisons are all within-family to eliminate confounding by population structure or racism/colorism/discrimination. The necessary sample size for well-powered studies is closely related to the average size of differences in ancestry percentage between siblings, as the upper bound on IQ effect per percentage is small, requiring large differences in ancestry to detect easily. A within-family comparison of siblings, due to the relatively small differences in ancestry between siblings estimated from IBD measurements of siblings, might require n > 50,000 pairs of siblings to detect possible effects on IQ, an infeasible sample size. An alternative design focuses on increasing the available ancestry differences within a family unit by comparing adoptees with siblings; the larger within-population standard deviation of ancestry creates larger & more easily-detected IQ differences. A random-effects meta-analysis of past admixture & ancestry studies suggests the SD in heterogeneous samples may range from 2% to 20% with a mean of 11% (95% predictive interval), yielding sample sizes of n > 20,000, n = 1100924ya, and n = 500. Hence, an adoption study is probably in the feasible range, with required sample sizes comparable to annual adoption rates among US African-Americans.

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