Two sample distribution-free inference based on partially rank-ordered set samples

This paper develops distribution-free inference for a location shift model based on a partially rank-ordered set (PROS) sample. In a PROS sample, a small set of experimental units is judgment ranked without measurement by allowing ties whenever the units cannot be ranked with high confidence. These tied units are replaced in partially ordered judgment subsets from which a unit is selected at random for a full measurement. Based on this sampling design, we construct an estimator, a test and a confidence interval for the location shift parameter. It is shown that the new sampling design is robust against any possible ranking error and has higher efficiency than competitor designs in the literature.