Improved randomized response technique for estimating population proportion of a sensitive characteristic

Abstract

Getting correct answers to sensitive questions from the respondents and estimating the population parameters on variables that are sensitive in nature is prevailing problem in survey sampling. In the present research paper, the problem of estimation of the population proportion of sensitive characteristics has been studied. For this, an improved randomized response device has been developed by taking the two cases of the unrelated question, case-I: ‘when the proportion of unrelated characteristic is known’ and other case-II: ‘when the proportion of unrelated characteristic is not known’. Two estimators of the population proportion of a sensitive characteristic have been proposed, one for a known value of unrelated characteristic ${\pi }_y$ and the other for an unknown value, which were found to be unbiased. The expression for variances and unbiased estimates for the variances of the proposed estimators have been obtained. The optimum value of sample sizes has been worked out for which the minimum variance for the proposed estimators has also been obtained. An empirical study has been conducted and concluded graphically that proposed estimators are better than the estimators of Mangat (1992) and Tiwari and Mehta (2016).