Overall, the χ2 test is most powerful at the nominal significance level, as expected, given the inflated false positive rate. Table IV shows the estimated power for the χ2 test and the corrected χ2 tests with ϕact, ϕped, ϕest and ϕpost. At the nominal significance level, the corrected χ2 test has lower power than the χ2 test, and in particular, the corrected χ2 test with ϕact has the least power. The corrected χ2 test with ϕest is more powerful than the corrected χ2 test with ϕped and ϕpost. This result shows that the correction for kinship may cause apparent loss of power given a nominal significance level. However the corrected tests give the proper null distribution of p-values as we showed previously. As a result, the test has the correct type I error in contrast to the χ2 test, which is too liberal. Because power in our simulation was estimated under the nominal significance level, but the tests have different type I errors, it is not meaningful to compare actual power in this situation.
