Ordinal dominance curve based inference for stochastically ordered distributions

Abstract

In a variety of applications researchers collect data that are sampled under ordered experimental conditions. In such situations it is reasonable to assume that outcomes are ordered stochastically by the level of the treatment. For example a toxicologist may want to assess the effect of a toxin on the reproductive system by studying the number of offspring produced by an animal as a function of the dose that it received. A variety of scientific questions arise in such a context. The most basic is whether a dose-response relationship is present. If so, determining the minimal toxic dose is of great interest. The strength of the ordering between groups i