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Sample Size Determination for Interval Estimation of the Prevalence of a Sensitive Attribute Under Randomized
Shi-Fang Qiu1, Man-Lai Tang2, Ji-Ran Tao3
1Department of Statistics, Chongqing University of Technology, Chongqing, 400054, China.
Psychometrika
|March 20, 2022
Summary
Determining the correct sample size is crucial for sensitive survey research. This study provides new sample size formulas for four randomized response models to ensure accurate prevalence estimation without wasting resources.
Area of Science:
- Statistics
- Survey Methodology
- Social Sciences
Background:
- Adequate respondent numbers are essential for sensitive research.
- Insufficient sample sizes yield inconclusive results, while excessive numbers waste budget.
- Determining optimal sample size is a critical step in survey design.
Purpose of the Study:
- To derive sample size formulas for four randomized response models.
- To ensure confidence interval width is controlled within a planned range.
- To provide practical tools for researchers conducting sensitive surveys.
Main Methods:
- Developed sample size formulas based on confidence interval estimation of prevalence.
- Utilized four distinct randomized response models: Warner's, unrelated question, item count technique, and cheater detection.
- Validated formulas through simulation studies assessing coverage and assurance probabilities.
Main Results:
- Derived accurate sample size formulas for the specified randomized response models.
- Simulation results confirmed the formulas' reliability in achieving desired precision.
- Demonstrated practical application using a real-world scenario on negotiation tactics.
Conclusions:
- The proposed sample size formulas effectively balance statistical rigor and resource efficiency.
- These formulas are valuable for researchers studying sensitive topics using randomized response techniques.
- Accurate sample size determination enhances the validity and impact of survey research findings.
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