In many genetics studies, especially in the investigation of mental illness and behavioral disorders, it is common for researchers to collect multiple phenotypes to characterize the complex disease of interest. It may be advantageous to analyze those phenotypic measurements simultaneously if they share a similar genetic mechanism. In this study, we present a nonparametric approach to studying multiple traits together rather than examining each trait separately. Through simulation we compared the nominal type I error and power of our proposed test to an existing test, i.e., a generalized family-based association test. The empirical results suggest that our proposed approach is superior to the existing test in the analysis of ordinal traits. The advantage is demonstrated on a data set concerning alcohol dependence. In this application, the use of our methods enhanced the signal of the association test.