Sample size determination for interval estimation of the prevalence of a sensitive attribute under non-randomized response models

Shi-Fang Qiu, Jie Lei, Wai-Yin Poon, Ricky Wong, Ji-Ran Tao

Research output: Contribution to journalArticlepeer-review

Abstract

A sufficient number of participants should be included to adequately address the research interest in the surveys with sensitive questions. In this paper, sample size formulas/iterative algorithms are developed from the perspective of controlling the confidence interval width of the prevalence of a sensitive attribute under four non-randomized response models: the crosswise model, parallel model, Poisson item count technique model and negative binomial item count technique model. In contrast to the conventional approach for sample size determination, our sample size formulas/algorithms explicitly incorporate an assurance probability of controlling the width of a confidence interval within the pre-specified range. The performance of the proposed methods is evaluated with respect to the empirical coverage probability, empirical assurance probability and confidence width. Simulation results show that all formulas/algorithms are effective and hence are recommended for practical applications. A real example is used to illustrate the proposed methods.
Original languageEnglish
Article number12338
Pages (from-to)1-24
Number of pages24
JournalBritish Journal of Mathematical and Statistical Psychology
Early online date26 Feb 2024
DOIs
Publication statusPublished - 26 Feb 2024

Keywords

  • assurance probability
  • confidence interval
  • non-randomized response models
  • sample size determination
  • sensitive attribute

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