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Benford’s Law: Textbook Exercises and Multiple-Choice Testbanks

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  • Aaron D Slepkov
  • Kevin B Ironside
  • David DiBattista

Abstract

Benford’s Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common leading digit is 1, with an expected frequency of 30.1%, and the least common is 9, with an expected frequency of 4.6%. Currently, the most common application of Benford’s Law is in detecting number invention and tampering such as found in accounting-, tax-, and voter-fraud. We demonstrate that answers to end-of-chapter exercises in physics and chemistry textbooks conform to Benford’s Law. Subsequently, we investigate whether this fact can be used to gain advantage over random guessing in multiple-choice tests, and find that while testbank answers in introductory physics closely conform to Benford’s Law, the testbank is nonetheless secure against such a Benford’s attack for banal reasons.

Suggested Citation

  • Aaron D Slepkov & Kevin B Ironside & David DiBattista, 2015. "Benford’s Law: Textbook Exercises and Multiple-Choice Testbanks," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-13, February.
    • Handle: RePEc:plo:pone00:0117972
    DOI: 10.1371/journal.pone.0117972
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    Cited by:

    1. Wang, Delu & Chen, Fan & Mao, Jinqi & Liu, Nannan & Rong, Fangyu, 2022. "Are the official national data credible? Empirical evidence from statistics quality evaluation of China's coal and its downstream industries," Energy Economics, Elsevier, vol. 114(C).
    2. Horton, Joanne & Krishna Kumar, Dhanya & Wood, Anthony, 2020. "Detecting academic fraud using Benford law: The case of Professor James Hunton," Research Policy, Elsevier, vol. 49(8).
    3. da Silva, A.J. & Floquet, S. & Santos, D.O.C. & Lima, R.F., 2020. "On the validation of the Newcomb−Benford Law and the Weibull distribution in neuromuscular transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    4. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Philip E Hulme & Danish A Ahmed & Phillip J Haubrock & Brooks A Kaiser & Melina Kourantidou & Boris Leroy & Shana M Mcdermott, 2024. "Widespread imprecision in estimates of the economic costs of invasive alien species worldwide," Post-Print hal-04633043, HAL.

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