Improved estimation method for mean and sensitivity through randomized response technique

Collecting truthful survey data regarding sensitive topics such as workplace harassment, undisclosed substance use, or financial evasion remains a persistent problem in social science research. This challenge is particularly severe in face-to-face interviews, where respondents often hesitate to answer honestly due to fears of public exposure and privacy concerns. Consequently, the inferences drawn from such biased or incomplete responses often lack reliability and accuracy. To address this, randomized response techniques (RRT’s) have been leveraged to offer a mathematical shield for privacy; however, they often fail in practice when respondents simply do not trust the scrambling mechanism used for randomization. To cover the gap between privacy protection and respondent trust, we propose a novel two-stage optional randomized response technique (ORRT) model. This tiered approach uniquely integrates a trust parameter in the model, offering skeptical respondents a safe alternative to provide direct responses rather than dropping out or resorting to deception. Through rigorous theoretical derivation and from extensive Monte Carlo simulations, we demonstrate that the proposed model performs the best among all existing estimators in accurately judging the population mean of sensitive variables. Although the model involves a tradeoff regarding the precision of sensitivity level estimation, it provides a superior solution for researchers prioritizing the accuracy of primary data while safeguarding maximum cooperation from respondents.