Stratified Randomized Response Sampling for Estimating Sensitive Proportions in Populations: An Enhanced Approach to Privacy and Precision

In surveys, social desirability bias and privacy concerns often hinder honest responses to sensitive questions. The randomized response technique (RRT) mitigates these issues by preserving respondent anonymity, but its conventional application under simple random sampling ignores population heterogeneity. This paper proposes a novel methodology that integrates stratified sampling with RRT to simultaneously improve estimation precision and protect privacy. By partitioning the population into homogeneous strata and applying RRT within each stratum, the proposed approach reduces response bias and yields more accurate estimates of sensitive proportions. Explicit formulas for estimating population proportions and variances are derived, and an optimal sample allocation rule is provided to minimize overall variance. A hypothetical survey on tax evasion illustrates the methodology, and a simulation study demonstrates that the proposed stratified RRT estimator achieves a relative efficiency of 2.34 (a 57% variance reduction) compared to conventional RRT under simple random sampling. The procedure is versatile and applicable in social sciences, public health, and other fields requiring confidential data collection.