A two-stage randomized response technique for simultaneous estimation of sensitivity and truthfulness

Privacy protection is a critical concern when dealing with sensitive survey questions. Conventional randomized response (RR) models frequently fall short in providing respondents with adequate secrecy when assessing important parameters like the probability of success p and the probability of truthfulness T. This study proposes an improved RR technique that addresses these drawbacks by providing better privacy protections and enabling the simultaneous calculation of T and π.The advantage of the proposed model is that it applies a two-stage randomization process, which estimates both T and π thereby offering enhanced protection for privacy. The proposed method is first initially developed using simple random sampling and builds upon a two-stage RR approach described in previous research. It is then expanded to include stratified random sampling in order to make it more applicable to survey designs that are more intricate. The methodology is derived analytically and evaluated with respect to computing efficiency and algebraic measures. The suggested model increases the overall quality and reliability of the survey data by reducing respondent reluctance and producing more accurate parameter estimations, as shown by efficiency comparisons with current methods. Additionally, without sacrificing the accuracy of the statistical estimates, the approach improves respondent participation. Simulations using different fixed values of n, π, and T show that the suggested model continuously performs better than traditional techniques in terms of reducing variance and protecting privacy under both simple and stratified sampling. These findings show that it is a useful, statistically sound method for carrying out surveys on delicate subjects, guaranteeing data quality and respondent protection.