We develop an unbiased estimator of the variance of a population based on a ranked set sample. We show that this new estimator is better than estimating the variance based on a simple random sample and more efficient than the estimator based on a ranked set sample proposed by Stokes. Also, a test to determine the effectiveness of the judgment ordering process is proposed. Copyright 2002 The Royal Statistical Society.
After the completion of many studies, experimental results are reported in terms of distribution‐free confidence intervals that may involve pairs of order statistics. This article considers a meta‐analysis procedure to combine these confidence intervals from independent studies to estimate or construct a confidence interval for the true quantile of the population distribution. Data synthesis is made under both fixed‐effect and random‐effect meta‐analysis models. We show that mean square error (MSE) of the combined quantile estimator is considerably smaller than that of the best individual quantile estimator. We also show that the coverage probability of the meta‐analysis confidence interval is quite close to the nominal confidence level. The random‐effect meta‐analysis model yields a better coverage probability and smaller MSE than the fixed‐effect meta‐analysis model. The meta‐analysis method is then used to synthesize medians of patient delays in pulmonary tuberculosis diagnosis in China to provide an illustration of the proposed methodology.
Ranked-set sampling from a finite population is considered in this paper. Three sampling protocols are described, and procedures for constructing nonparametric confidence intervals for a population quantile are developed. Algorithms for computing coverage probabilities for these confidence intervals are presented, and the use of interpolated confidence intervals is recommended as a means to approximately achieve coverage probabilities that cannot be achieved exactly. A simulation study based on finite populations of sizes 20, 30, 40, and 50 shows that the three sampling protocols follow a strict ordering in terms of the average lengths of the confidence intervals they produce. This study also shows that all three ranked-set sampling protocols tend to produce confidence intervals shorter than those produced by simple random sampling, with the difference being substantial for two of the protocols. The interpolated confidence intervals are shown to achieve coverage probabilities quite close to their nominal levels. Rankings done according to a highly correlated concomitant variable are shown to reduce the level of the confidence intervals only minimally. An example to illustrate the construction of confidence intervals according to this methodology is provided.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.