The genome-wide association studies have improved our understanding of the genetic basis of many complex traits. Two-by-three contingency tables are tested in these studies. The trend test for the additive mode is most often used, which is the test of 1 degree of freedom (df=1) and other tests, such as the genotype test (chi(2) (df=2)) and the chi(2) (df=1) tests for the dominant and recessive modes are also used to increase the power for markers in the non-additive modes. However, any one of them or combination of them is not perfect. We describe the relations among the chi(2) (df=2) test and chi(2) (df=1) tests for the dominant and recessive modes and the trend test for the additive mode and propose a new statistic based on their relations that tests the hypothesis that the disease-susceptible allele has a dose-effect somewhere between the recessive and dominant modes, which corresponds to the optimal dose-effect for the observed data.