A Nontransitive Paradox in the Nonparametric Setting

In statistics, when performing a nonparametric test on multiple samples, a nontransitive paradox can emerge. For example, given three samples we might find that sample A performs better than sample B, B performs better than C, but C performs better than A. We discuss this phenomenon using the example of a set of 'nontransitive dice' and explore how to resolve the paradox by using a reference die.