Ranked set sampling for efficient estimation of a population proportion

Ranked set sampling (RSS) is a sampling procedure that can be considerably more efficient than simple random sampling (SRS). It involves preliminary ranking of the variable of interest to aid in sample selection. Although ranking processes for continuous variables that are implemented through either subjective judgement or via the use of a concomitant variable have been studied extensively in the literature, the use of RSS in the case of a binary variable has not been investigated thoroughly. In this paper we propose the use of logistic regression to aid in the ranking of a binary variable of interest. We illustrate the application of RSS to estimation of a population proportion with an example based on the National Health and Nutrition Examination Survey III data set. Our results indicate that this use of logistic regression improves the accuracy of the preliminary ranking in RSS and leads to substantial gains in precision for estimation of a population proportion.