The equivalence between Mann-Whitney Wilcoxon test and score test based on the proportional odds model for ordinal responses

The two-group comparison remains to be one of the most basic tasks in statistical analysis. In comparing the distribution of ordinal responses between two groups, Mann-Whitney Wilcoxon test is often used for hypothesis testing, while the proportional odds model is employed for characterizing the between group difference. This synthetic approach raises an important question that whether the results from these two methods are always consistent in analyzing the same data. In this paper, we provide the theoretical justification that both the nonparametric Mann-Whitney Wilcoxon test and the score test of the proportional odds model depends on the proportion of pairs in which the response from one group is higher than that in another group and are equivalent. This result guarantees the asymptotical consistency of the two steps of the synthetic approach. We also use simulation study and real data example to further confirm the equivalence of two tests in finite samples.