Ranked Set Sampling for a Population Proportion:Allocation of Sample Units to Each Judgment Order Statistic

Abstract

Ranked set sampling is an alternative to simple random sampling that has been shown to outperform simple random sampling in many situations by reducing the variance of an estimator, thereby providing the same accuracy with a smaller sample size than is needed in simple random sampling. Ranked set sampling involves preliminary ranking of potential sample units on the variable of interest using judgment or an auxiliary variable to aid in sample selection. Ranked set sampling prescribes the number of units from each rank order to be measured. Balanced ranked set sampling assigns equal numbers of sample units to each rank order. Unbalanced ranked set sampling allows unequal allocation to the various ranks, but this allocation may be sensitive to the quality of information available to do the allocation. In this paper we use a simulation study to conduct a sensitivity analysis of optimal allocation of sample units to each of the order statistics in unbalanced ranked set sampling. Our motivating example comes from the National Survey of Families and Households.