The association analysis between the disease and alleles is one of the simple methods for localizing the susceptibility genes. For revealing the association, several statistical tests have been proposed without discussing explicitly the alternative hypotheses. We therefore specify two types of alternative hypotheses: 1. there is only one susceptibility gene in the locus; 2. there is an extension or shortening of alleles associated with disease, and derive exact maximal chi-squared type tests for the respective hypotheses. We also propose to combine those two tests when the prior knowledge in not sufficient enough to specify one of those two hypotheses. Inparticular those ideas are extended to the three-way association between the disease and bivariate allele frequencies at two closely linked loci.