A generalized approach to randomised response for quantitative variables

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• 作者：Antonio Arcos ; María del Mar Rueda ; Sarjinder Singh
• 关键词：Sensitive question ; Randomised response technique ; Sampling design ; Social surveys
• 刊名：Quality & Quantity
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：49
• 期：3
• 页码：1239-1256
• 全文大小：1,030 KB
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  Warner,
• 作者单位：Antonio Arcos (1)
  María del Mar Rueda (1)
  Sarjinder Singh (2)
  
  1. University of Granada, Granada, Spain
  2. Texas A&M University at Kingsville, Kingsville, USA
  
• 刊物类别：Humanities, Social Sciences and Law
• 刊物主题：Social Sciences
  Methodology of the Social Sciences
  Social Sciences
  
• 出版者：Springer Netherlands
• ISSN：1573-7845

文摘

The methodology of randomised response (RR) has advanced considerably in recent years. Nevertheless, most research in this area has addressed the estimation of qualitative variables, and relatively little attention has been paid to the study of quantitative ones. Furthermore, most studies concern only simple random sampling. In this paper, we present a new model of RR aimed at determining a total that is valid for any sampling design. This general procedure includes several important RR techniques that constitute particular cases. We propose an unbiased estimator, with an analytic expression for its variance. Confidence intervals are also obtained for the parameter, applying analytical formulae such as those based on resampling technologies. A simulation study illustrates the behaviour of the estimator using diverse randomisation devices and for different scrambling distributions. To illustrate the advantages of this method, we obtained a stratified clustered sample of university students, who were questioned to determine the frequency with which they cheated in exams. Their responses to these questions were obtained via an RR technique, and also using a direct questionnaire. We conclude that estimates based on anonymous questionnaires may result in severe underestimation.