Relationship between the distributions of allele frequency differences and disease association statistics, if cases and controls are drawn from distinct populations. We provide a mathematical derivation for the result that a null distribution of allele frequency differences implies a null distribution of disease association statistics after correction by genomic control. We consider a hypothetical association study in which N/2 diploid disease cases are drawn from population 1 and N/2 diploid controls are drawn from population 2. Any instance of population stratification can be considered in this framework by defining population 1 and population 2 as appropriate admixtures of the underlying populations. For a given marker, let p 1 and p 2 denote observed frequencies in cases and controls and p be the mean of p 1 and p 2. It follows that the correlation between genotype and case-control status is equal to, so that the Cochran-Armitage trend statistic [38], which equals N times the square of that correlation, is equal to. Since (p 1−p 2) is normally distributed with mean 0 and variance p(1−p)(2F ST+1/N 1+1/N 2), where N 1
