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A New Benford Test for Clustered Data with Applications to American Elections

Author

Listed:
  • Katherine M. Anderson

    (Department of Economics, Brigham Young University-Idaho, 298 S 1st East SMI 214, Rexburg, ID 83460, USA)

  • Kevin Dayaratna

    (Center for Data Analysis, The Heritage Foundation, 214 Massachusetts Ave. NE, Washington, DC 20002, USA)

  • Drew Gonshorowski

    (Center for Data Analysis, The Heritage Foundation, 214 Massachusetts Ave. NE, Washington, DC 20002, USA)

  • Steven J. Miller

    (Department of Mathematics and Statistics, Williams College, 880 Main St., Williamstown, MA 01267, USA)

Abstract

A frequent problem with classic first digit applications of Benford’s law is the law’s inapplicability to clustered data, which becomes especially problematic for analyzing election data. This study offers a novel adaptation of Benford’s law by performing a first digit analysis after converting vote counts from election data to base 3 (referred to throughout the paper as 1-BL 3), spreading out the data and thus rendering the law significantly more useful. We test the efficacy of our approach on synthetic election data using discrete Weibull modeling, finding in many cases that election data often conforms to 1-BL 3. Lastly, we apply 1-BL 3 analysis to selected states from the 2004 US Presidential election to detect potential statistical anomalies.

Suggested Citation

  • Katherine M. Anderson & Kevin Dayaratna & Drew Gonshorowski & Steven J. Miller, 2022. "A New Benford Test for Clustered Data with Applications to American Elections," Stats, MDPI, vol. 5(3), pages 1-15, August.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:3:p:49-855:d:903399
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    References listed on IDEAS

    as
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    4. Engel, Hans-Andreas & Leuenberger, Christoph, 2003. "Benford's law for exponential random variables," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 361-365, July.
    5. Theoharry Grammatikos & Nikolaos I. Papanikolaou, 2021. "Applying Benford’s Law to Detect Accounting Data Manipulation in the Banking Industry," Journal of Financial Services Research, Springer;Western Finance Association, vol. 59(1), pages 115-142, April.
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