ARSTRACTTwo general welfare criteria, mean‐relative Lorenz and mean‐absolute Lorenz dominance, induce partial orders on income distributions. We propose asymptotically distribution‐free inference procedures, based on the union‐intersection principle, for these two welfare criteria. Unlike classical tests, our procedures allow one to distinguish among dominance, equality, and noncomparability. We show that union‐intersection tests must be used to test for partial orders, and that the statistical ordering is acyclic. The tests are applied to compare the UK distribution of real family income to five other