The Optimal Sample Size in Crosswise Model for Sensitive Questions
Stanis{\l}aw Jaworski, Wojciech Zieli\'nski
TL;DR
This paper analyzes the nonrandomized response model for estimating the proportion of a population with a stigmatizing trait, deriving an exact confidence interval and the optimal sample size for precise estimation.
Contribution
It introduces an exact confidence interval and determines the optimal sample size for the nonrandomized response model in sensitive question surveys.
Findings
Exact confidence interval for the population proportion is constructed.
Optimal sample size for desired confidence interval length is derived.
Method improves accuracy in estimating sensitive characteristics.
Abstract
The problem is in the estimation of the fraction of population with a stigmatizing characteristic. In the paper the nonrandomized response model proposed by Tian, Yu, Tang, and Geng (2007) is considered. The exact confidence interval for this fraction is constructed. Also the optimal sample size for obtaining the confidence interval of a given length is derived.
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Taxonomy
TopicsSurvey Sampling and Estimation Techniques