Comparing several robust tests of stochastic equality with ordinally scaled variables and small to moderate sized samples

In a comparison of 2 treatments, if outcome scores are denoted by X in 1 condition and by Y in the other, stochastic equality is defined as P(X < Y) = P(X > Y). Tests of stochastic equality can be affected by characteristics of the distributions being compared, such as heterogeneity of variance. Thus, various robust tests of stochastic equality have been proposed and are evaluated here using a Monte Carlo study with sample sizes ranging from 10 to 30. Three robust tests are identified that perform well in Type I error rates and power except when extremely skewed data co-occur with very small n. When tests of stochastic equality might be preferred to tests of means is also considered.