The transmission disequilibrium test uses association between marker alleles and dichotomous traits for precise genetic mapping while avoiding confounding due to population admixture. Here, the methodology is generalized from dichotomous traits to quantitative traits. The generalization is computationally straightforward and may be used with multiple alleles and with siblings. Parametric assumptions on the distribution of the quantitative traits are not needed. Environmental and demographic covariates may be incorporated into the analysis. The results of simulation studies that provide information about the power of the approach are reported.