Two stage ranked set sampling for estimating the population median

McIntyre was the first to suggest ranked set sampling (RSS) method for estimating the population mean. In this paper, we modify RSS to come up with new sampling method, namely, two stage ranked set sampling (TSRSS) for samples of size m = 3k (k = 1, 2,...). The TSRSS is suggested for estimating the population median in order to increase the efficiency of the estimators. The TSRSS was compared to the simple random sampling (SRS), ranked set sampling (RSS), extreme ranked set sampling (ERSS), median ranked set sampling (MRSS) and balance groups ranked set sampling (BGRSS) methods. It is found that, TSRSS gives an unbiased estimator of the population median of symmetric distributions and it is more efficient than SRS. Also, it is more efficient than RSS, ERSS, MRSS and BGRSS based on the same number of measured units. For asymmetric distributions considered in this study, TSRSS has a small bias and smaller variance than SRS, RSS, ERSS, MRSS and BGRSS methods.