According to wikipedia and other scattered software documentation Kruskal Wallis tests assess "stochastic dominance". But the original paper doesn't mention "dominance". Nor does Dunn's much-cited 1964 paper. A stata function documentation mentions that it tests dominance "that is, the probability that a randomly drawn observation from one group will be greater than a randomly drawn observation from another." here. Does that relate to the different formal types of stochastic dominance, e.g. from decision theory here? Can someone help clarifying what approaches there are to assess stochastic dominance (properly-defined) and particulary how and why are they related to Kruskal Wallis type approaches. Ideally a modern reference to clarify. Many thanks for the pointers!
