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Making Use of “Benford’s Law†for the Randomized Response Technique

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  • Andreas Diekmann

Abstract

In this article, “Benford’s law†is applied to the “randomized response technique†(RRT) to increase the validity of answers to sensitive questions. Using the Newcomb–Benford distribution as a randomizing device has several advantages. It is easy to explain and follow the procedure, as no physical device such as a coin or a dice is necessary and the method guarantees full anonymity. As is well known, the price for the anonymity of the RRT is a decrease in the efficiency of the estimator. However, because of the subjective overestimation of certain numbers (Benford illusion), the conflict between the variance of the estimates and the degree of anonymity is less pronounced compared to other RRT methods. The suggested RRT variant has the potential to improve the efficiency of the estimator. Moreover, the assumption is that this method works well with self-administered questionnaires.

Suggested Citation

  • Andreas Diekmann, 2012. "Making Use of “Benford’s Law†for the Randomized Response Technique," Sociological Methods & Research, , vol. 41(2), pages 325-334, May.
    • Handle: RePEc:sae:somere:v:41:y:2012:i:2:p:325-334
    DOI: 10.1177/0049124112452525
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    References listed on IDEAS

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    1. Andreas Diekmann, 2007. "Not the First Digit! Using Benford's Law to Detect Fraudulent Scientif ic Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(3), pages 321-329.
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    Cited by:

    1. Andreas Quatember, 2019. "A discussion of the two different aspects of privacy protection in indirect questioning designs," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(1), pages 269-282, January.
    2. Marc Höglinger & Ben Jann, 2016. "MTurk Survey on "Mood and Personality". Documentation," University of Bern Social Sciences Working Papers 17, University of Bern, Department of Social Sciences.
    3. Kundt, Thorben, 2014. "Applying “Benford’s law” to the Crosswise Model: Findings from an online survey on tax evasion," Working Paper 148/2014, Helmut Schmidt University, Hamburg.
    4. Marc Höglinger & Ben Jann, 2018. "More is not always better: An experimental individual-level validation of the randomized response technique and the crosswise model," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-22, August.
    5. Marc Höglinger & Ben Jann & Andreas Diekmann, 2014. "Online Survey on "Exams and Written Papers". Documentation," University of Bern Social Sciences Working Papers 8, University of Bern, Department of Social Sciences, revised 06 Oct 2014.

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