Statistica Sinica 25 (2015), 1691-1712
Abstract: A distribution-free procedure is developed to test a stochastic order relation between two distributions based on judgment post-stratified (JPS) data. The proposed inference relies on Mann-Whitney rank sum statistics. A first class of tests constructs test statistics by comparing all units in both samples, while a second class first stratifies the data into judgment classes and then constructs a rank sum statistic in each stratum, with the final test statistic constructed from a linear combination of these within-judgment class rank sum statistics. Distributional properties of the testing procedures are investigated. The null distributions of the test statistics in the first class depend on the quality of ranking information while the null distributions of the test statistics in the second class are distribution-free for any sample sizes, regardless of the quality of ranking information. Both tests have higher efficiencies than corresponding tests based on a simple random sample rank sum statistic. For large samples, testing procedures in the first and second classes are equivalent, respectively, to Bohn-Wolfe and Fligner-MacEachern testing procures in a ranked set sampling design.
Key words and phrases: Calibration, imperfect ranking, Mann-Whitney, ranked-set sampling, rank sum test, stochastic order.