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A generalized approach to randomised response for quantitative variables

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Abstract

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.

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Acknowledgments

This study was partially supported by Ministerio de Educación y Ciencia (grant MTM2012-35650, Spain) and by Consejería de Economía, Innovación, Ciencia y Empleo (grants SEJ2954 and HUM1413 Junta de Andalucía).

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Authors and Affiliations

  1. University of Granada, Granada, Spain

    Antonio Arcos & María del Mar Rueda

  2. Texas A&M University at Kingsville, Kingsville, USA

    Sarjinder Singh

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  1. Antonio Arcos
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  2. María del Mar Rueda
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  3. Sarjinder Singh
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Correspondence to María del Mar Rueda.

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Arcos, A., Rueda, M.M. & Singh, S. A generalized approach to randomised response for quantitative variables. Qual Quant 49, 1239–1256 (2015). https://doi.org/10.1007/s11135-014-0046-3

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