The Stochastic Inequality Test - a Test for a Directional Treatment Effect

The stochastic inequality test is an exact non-parametric test that can be used to infer whether values in one random sample tend to be higher than in another. In addition it can be used to derive a confidence interval around an intuitive measure of effect size that is readily interpretable forboth ordinal and cardinal data, and allows for \textit{ex-ante} power analysis. Unlike other commonly used tests, such as the t-test and the Wilcoxon-Mann-Whitney test, this inference is valid without requiring additional, often unrealistic and untestable, assumptions about the shape of the underlying population distributions