Abstract: In order to test the symmetric point of an infinite population, a Wilcoxon signed-rank test statistic based on ranked set sampling with unequal samples is constructed. Its distribution is shown to be symmetric and distribution-free under null hypothesis. The asymptotic normality of the new test statistic is proved, and its Pitman efficiency factor is given. The calculated results of Pitman asymptotic relative efficiencies show that the new test is superior to the signed-rank tests under simple random sampling and ranked set sampling.

Key words: ranked set sampling, signed-rank test, Pitman efficiency, simple random sampling