The analysis of genome-wide genetic association studies generally starts with univariate statistical tests of each single-nucleotide polymorphism. The standard approach is the Cochran-Armitage trend test or its logistic regression equivalent although this approach can lose considerable power if the underlying genetic model is not additive. An alternative is the MAX test, which is robust against the three basic modes of inheritance. Here, the asymptotic distribution of the MAX test is derived using the generalized linear model together with the Delta method and multiple contrasts. The approach is applicable to binary, quantitative, and survival traits. It may be used for unrelated individuals, family-based studies, and matched pairs. The approach provides point and interval effect estimates and allows selecting the most plausible genetic model using the minimum P-value. R code is provided. A Monte-Carlo simulation study shows that the asymptotic MAX test framework meets type I error levels well, has good power, and good model selection properties for minor allele frequencies ≥0.3. Pearson's χ(2)-test is superior for lower minor allele frequencies with low frequencies for the rare homozygous genotype. In these cases, the model selection procedure should be used with caution. The use of the MAX test is illustrated by reanalyzing findings from seven genome-wide association studies including case-control, matched pairs, and quantitative trait data.