The locally most powerful test among all tests with the correct type I errors is the score test (Cox and Hinkley, 1974) which sets a standard other tests can be compared to. For allele-based analysis, ESS-corrected Xe2 is identical to the score test, sharing the same power. For genotype-based test (i.e. chi-square test on 2-by-3 genotype count table), chi-square test using ESS-corrected Xe2 is not identical to the score test. Here we adopt the simplest ESS correction for genotype data: multiplying the genotype counts by a constant reduction value ᾱ = 0.7096. The power curve in Figure 3 shows that the difference between the ESS-corrected Xe2 test and score test is negligible for dominant or additive disease models. The difference for recessive models is non-zero, but nevertheless small.
