Department of Statistics, Chongqing University of Technology, Chongqing, 400054, China.
Department of Mathematics, Brunel University London, Uxbridge, UB8 3PH, UK.
Psychometrika. 2022 Dec;87(4):1361-1389. doi: 10.1007/s11336-022-09854-w. Epub 2022 Mar 20.
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.
对于涉及敏感问题的研究，应该有足够数量的受访者来充分解决研究兴趣。虽然受访者数量不足的研究可能不会得出有意义的结论，但受访者数量过多的研究也会浪费调查人员的预算。因此，在调查抽样中确定所需的参与者数量是一个重要步骤。在本文中，我们根据四种随机反应模型（即 Warner 随机反应模型、无关问题模型、项目计数技术模型和骗子检测模型）的流行率置信区间估计推导出样本量公式。具体来说，我们的样本量公式以给定的置信概率控制置信区间的宽度在计划范围内。模拟结果表明，所有公式在经验覆盖概率和经验保证概率方面都是准确的。所有公式都通过一个关于在谈判中使用不道德策略的实际应用来说明。
