Parameter Estimation in Stratified Cluster Sampling under Randomized Response Models for Sensitive Question Survey

Randomized response is a research method to get accurate answers to sensitive questions in structured sample survey. Simple random sampling is widely used in surveys of sensitive questions but hard to apply on large targeted populations. On the other side, more sophisticated sampling regimes and corresponding formulas are seldom employed to sensitive question surveys. In this work, we developed a series of formulas for parameter estimation in cluster sampling and stratified cluster sampling under two kinds of randomized response models by using classic sampling theories and total probability formulas. The performances of the sampling methods and formulas in the survey of premarital sex and cheating on exams at Soochow University were also provided. The reliability of the survey methods and formulas for sensitive question survey was found to be high.