Wilcoxon Signed Rank Test For Quantiles Under Ranked Ordering-Set Sample

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A ranked set sample version of the Wilcoxon signed rank test is proposed for testing hypotheses concerning the quantiles of a population characteristic by Kim and Kim(2003). In this paper, we propose the Wilcoxon signed rank test for quantiles under ranked ordering-set sample. We obtain the asymptotic properties and the asymptotic relative efficiencies of the proposed test statistic with respect to that of ranked set sample and simple random sample for quantiles under equal allocation. We calculate the ARE of test statistics, from the results the proposed test statistic is more efficient than that of ranked set sampling for all quantiles except the case that the value of quantiles and sample size are small. The relative advantage of ranked set sampling is greatest at the median and tapers off in the tails.