The ratio of two chi-squares, one for all samples with ESS correction and another without, is calculated to be Xe2/X2=45.73/53.26=0.86. This ratio can also be approximately estimated from ESS. Since X2 and Xe2 can be written in the form: X2 = (p̂A,case − p̂A,control)2/[(1/Ncase + 1/Ncontrol)·p̄·q̄], Xe2≈(p^A,case−p^A,control)2/[(1/(αNcase)+1/Ncontrol)·p¯·q¯] (in an approximation, the pooled allele frequency estimation for A and B is not greatly affected by the change of sample size), Xe2/X2≈(1/0.7×1680)+1/1852)/(1/1680+1/1852)=0.82.
