Ordered inference, rank statistics and combining pp-values: A new perspective

A family of simple two sample rank tests for testing for stochastic order is introduced. The proposed tests are motivated by the stochastic ordering of the ranks and methods for combining pp-values which capitalize on this ordering. We show that the new tests coincide with some well known rank tests. Their large sample distributions are derived under various assumptions on the sample sizes. Some optimality properties are discussed. Simulations show that the new tests perform well, often better than specialized tests designed for testing for order among two populations.