A modified unrelated question randomized response device for complex surveys

Abstract

Singh et al. (Stat Trans 6(4):515–522, 2003) proposed a modified unrelated question procedure and they also demonstrated that the modified procedure is capable of producing a more efficient estimator of the population parameter π _A , namely, the proportion of persons in a community bearing a sensitive character A when π _A  < 0.50. The development of Singh et al. (Stat Trans 6(4):515–522, 2003) is based on simple random samples with replacement and on the assumption that π _B , namely, the proportion of individuals bearing an unrelated innocuous character B is known. Due to these limitations, Singh et al.’s (Stat Trans 6(4):515–522, 2003) procedure cannot be used in practical surveys where usually the sample units are chosen with varying selection probabilities. In this article, following Singh et al. (Stat Trans 6(4):515–522, 2003) we propose an alternative RR procedure assuming that the population units are sampled with unequal selection probabilities and that the value of π _B is unknown. A numerical example comparing the performance of the proposed RR procedure under alternative sampling designs is also reported.