Sign Tests Using Ranked Set Sampling with Unequal Samples

To test the median of an infinite population, a sign test based on ranked set sampling with unequal samples was proposed. According to compare the Pitman efficiencies of sign tests, the ranked set sampling with unequal samples is more efficient than ranked set sampling and the simple random sampling. Considering observations of ranked set sample with unequal samples are independent but not identically distributed, weighted sign tests in which weights associate with the judgment rank were presented, the weight that maximizes the test efficiency was identified and shown to be distribution-free. The computational results of Pitman relative efficiencies showed that the optimal weighted sign test under ranked set sampling with unequal samples is superior to the optimal weighted sign test under ranked set sampling. Finally, a practical application for a real data set related to a pine hardwood forest is made.