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Sample Size Determination for Interval Estimation of the Prevalence of a Sensitive Attribute Under Randomized Response Models

Author

Listed:
  • Shi-Fang Qiu

    (Chongqing University of Technology)

  • Man-Lai Tang

    (Brunel University London)

  • Ji-Ran Tao

    (Beijing Institute of Technology)

  • Ricky S. Wong

    (University of Hertfordshire)

Abstract

Studies with sensitive questions should include a sufficient number of respondents to adequately address the research interest. While studies with an inadequate number of respondents may not yield significant conclusions, studies with an excess of respondents become wasteful of investigators’ budget. Therefore, it is an important step in survey sampling to determine the required number of participants. In this article, we derive sample size formulas based on confidence interval estimation of prevalence for four randomized response models, namely, the Warner’s randomized response model, unrelated question model, item count technique model and cheater detection model. Specifically, our sample size formulas control, with a given assurance probability, the width of a confidence interval within the planned range. Simulation results demonstrate that all formulas are accurate in terms of empirical coverage probabilities and empirical assurance probabilities. All formulas are illustrated using a real-life application about the use of unethical tactics in negotiation.

Suggested Citation

  • Shi-Fang Qiu & Man-Lai Tang & Ji-Ran Tao & Ricky S. Wong, 2022. "Sample Size Determination for Interval Estimation of the Prevalence of a Sensitive Attribute Under Randomized Response Models," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1361-1389, December.
    • Handle: RePEc:spr:psycho:v:87:y:2022:i:4:d:10.1007_s11336-022-09854-w
    DOI: 10.1007/s11336-022-09854-w
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    References listed on IDEAS

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    1. Jun-Wu Yu & Guo-Liang Tian & Man-Lai Tang, 2008. "Two new models for survey sampling with sensitive characteristic: design and analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 251-263, April.
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