Two Sample Distribution-Free Inference Based on Partially Rank Ordered Set Sample Keywords: Imperfect ranking, ranking models, judgment subsets, rank-sum-test This study develops distribution free inference for a location shift model based on a special sampling design. The new sampling design, in pincipal, is similar to a ranked set sampling, with some clear di?erences. In the construction of a sample with the new design, a small set of experimental units are judgment ranked without measurement by allowing ties whenever the units can not be ranked with high con?dence. These tied units are replaced in judgment subsets. The fully measured units are then selected from these partially ordered judgment subsets. Based on this sampling design, we construct an estimator, a test and a con?dence interval for the location shift parameter. It is shown that the new sampling design is robust against any possible ranking error and has higher e?ciency than its competitor designs in the literature.
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