Case-control studies are primary study designs used in genetic association studies. Sasieni (Biometrics 1997, 53, 1253-1261) pointed out that the allelic chi-square test used in genetic association studies is invalid when Hardy-Weinberg equilibrium (HWE) is violated in a combined population. It is important to know how much type I error rate is deviated from the nominal level under violated HWE. We examine bounds of type I error rate of the allelic chi-square test. We also investigate power of the goodness-of-fit test for HWE which can be used as a guideline for selecting an appropriate test between the allelic chi-square test and the modified allelic chi-square test, the latter of which was proposed for cases of violated HWE. In small samples, power is not large enough to detect the Wright's inbreeding model of small values of inbreeding coefficient. Therefore, when the null hypothesis of HWE is barely accepted, the modified test should be considered as an alternative method.