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Digital Analysis of Crime Statistics: Does Crime Conform to Benford’s Law?

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Abstract

Benford’s law suggests that the distribution of leading (leftmost) digits in data of an anomalous nature (i.e., without relationship) will conform to a formula of logarithmic intervals known as the Benford distribution. Forensic auditors have successfully used digital analysis vis-à-vis the Benford distribution to detect financial fraud, while government investigators have used a corollary of the distribution (focused on trailing digits) to detect scientific fraud in medical research. This study explored whether crime statistics are Benford distributed. We examined crime statistics at the National, State, and local level in order to test for conformity to the Benford distribution, and found that National- and State-level summary UCR data conform to Benford’s law. When National data were disaggregated by offense type we found varying degrees of conformity, with murder, rape, and robbery indicating less conformity than other offense types. Some tentative implications of these findings are discussed, as are areas for further research.

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Notes

  1. The lead author participated in an investigation in which it was alleged that the subject agency had fraudulently received funding under the Justice Assistance Grant (JAG) program. However, the subject agency was suspected of under-reporting crime. This would have led to less funding under JAG; an agency seeking greater funding would need to over-report crime.

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Acknowledgments

This research was supported by a student research assistantship from the College of Arts & Sciences, Seattle University; the authors thank Laura Polson for her assistance in preparing this manuscript. The authors also thank James Lynch and the anonymous reviewers for their comments. Any errors are those of the authors.

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Authors and Affiliations

  1. Department of Criminal Justice, Seattle University, 901 12th Ave, PO Box 222000, Seattle, WA, 98122, USA

    Matthew J. Hickman & Stephen K. Rice

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  1. Matthew J. Hickman
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  2. Stephen K. Rice
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Correspondence to Matthew J. Hickman.

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Hickman, M.J., Rice, S.K. Digital Analysis of Crime Statistics: Does Crime Conform to Benford’s Law?. J Quant Criminol 26, 333–349 (2010). https://doi.org/10.1007/s10940-010-9094-6

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