A fundamental way of characterizing how two independent compares compare is in terms of the probability that a randomly sampled observation from the first group is less than a randomly sampled observation from the second group. The paper suggests a bivariate analog and investigates methods for computing confidence intervals. An interaction for a two-by-two design is investigated as well.
Wilcox, R. (2019). Bivariate analogs of the Wilcoxon–Mann–Whitney test and the Patel–Hoel method for interactions. Journal of Modern Applied Statistical Methods, 18(1), eP3129. doi: 10.22237/jmasm/1556669880