Ranked Set Sampling Based on Binary Water Quality Data with Covariates

A ranked set sample (RSS) is composed of independent order statistics, formed by collecting and ordering independent subsamples, then measuring only one item from each subsample. If the cost of sampling is dominated by data measurementrather than collection or ranking, the RSS technique is known to be superior to ordinary sampling. Experiments based on binary data are not designed to exploit the advantages of ranked set sampling because categorical data typically are as easily measured as ranked, making RSS methods impractical.However, in some environmentaland biologicalstudies, the success probability of a bivariate outcome is related to one or more covariates. If the covariate information is not easily quantied, but can be objectivelyordered with respect to this success probability, the RSS method can be used to improve the analysis of binary data. This article considers the case in which the covariate information is modeled in terms of a mixing distribution for the success probability, and the expected success probability is of primary interest. The inference technique is demonstrated with water-quality data from the Rappahannock river in Virginia. In a general setting, the RSS estimator is shown to be superior, including cases in which error in judgment ranking is present.