Using the simulated data described in the Methods and Material section, we have checked the validity of the effective sample size method. We first compare the test errors in using the uncorrected chi-square test statistic X2 and the ESS-corrected Xe2, for the allele-based test. Table 3 shows the type I error under the null distribution in chi-square test using the naive X2 and ESS-corrected Xe2. Note that for the null distribution, different disease model has no effect on the allele/genotype frequencies, and we simply consider the R/A/D models in Table 3 as three independent runs. It is clear that Xe2 leads to the more correct type I errors, practically identical to the nominal significance, whereas the naive X2 clearly leads to larger type I errors.
