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 = N 2 = N (see above), it follows that the Cochran-Armitage trend statistic has a χ2 (1 d.o.f.) distribution scaled by (1+NF ST). (See [39] for a related derivation.) This means that when the method of genomic control [40] is applied, the inflation factor λ is equal to 1+NF ST, and that dividing association statistics by λ results in a χ2 (1 d.o.f.) distribution. More generally, the fact that both the allele frequency difference statistic and the Cochran-Armitage trend statistic are proportional to (p 1−p 2)2/(p(1−p)) implies that the distributions of these two statistics are identical up to a constant scaling factor, even when allele frequency differences do not follow a null distribution.
