The Unbalanced Modified Ranked Ordering-Set Sample Sign Test

This paper introduces the modified ranked ordering-set sampling(MROSS) method which adds to supplement the independence of observations under ranked ordering-set sampling(ROSS). We are concerned with the sign test under unbalanced modified ranked ordering-set sampling(UMROSS), which constitutes a generalization of the modified ranked ordering-set sampling (MROSS). The null distribution properties of the MROSS and the UMROSS sign test are considered. The asymptotic relative efficiency of MROSS sign test with respect to ROSS sign test is always greater than 1. We consider a simple model to describe the effect of imperfect judgement ranking error. The UMROSS sign test optimizing the asymptotic relative efficiency criterion is discussed. The results strongly encourage the use of the optimized UMROSS sign test.