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

Shi-Fang Qiu (), Man-Lai Tang (), Ji-Ran Tao () and Ricky S. Wong ()
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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

Psychometrika, 2022, vol. 87, issue 4, No 8, 1389 pages

Abstract: 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.

Keywords: assurance probability; confidence interval; randomized response models; sample size determination; sensitive attribute (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11336-022-09854-w

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