Using residual heat maps to visualise Benford’s multi-digit law

Hull, Benjamin; Long, Alexander; Hughes, Ifan G

Abstract

It has been known for more than a century that, counter to one's intuition, the frequency of occurrence of the first significant digit in a very large number of numerical data sets is nonuniformly distributed. This result is encapsulated in Benford's law, which states that the first (and higher) digits follow a logarithmic distribution. An interesting consequence of the counter intuitive nature of Benford's law is that manipulation of data sets can lead to a change in compliance with the expected distribution—an insight that is exploited in forensic accountancy and financial fraud. In this investigation we have applied a Benford analysis to the distribution of price paid data for house prices in England and Wales pre and post-2014. A residual heat map analysis offers a visually attractive method for identifying interesting features, and two distinct patterns of human intervention are identified: (i) selling property at values just beneath a tax threshold, and (ii) psychological pricing, with a particular bias for the final digit to be 0 or 5. There was a change in legislation in 2014 to soften tax thresholds, and the influence of this change on house price paid data was clearly evident.

Citation

Hull, B., Long, A., & Hughes, I. G. (2022). Using residual heat maps to visualise Benford’s multi-digit law. European Journal of Physics, 43(1), Article 015803. https://doi.org/10.1088/1361-6404/ac3671

• Journal Article Type: Article
• Acceptance Date: Nov 4, 2021
• Online Publication Date: Nov 20, 2021
• Publication Date: 2022-01
• Deposit Date: Jan 27, 2022
• Publicly Available Date: Feb 1, 2022
• Journal: European Journal of Physics
• Print ISSN: 0143-0807
• Electronic ISSN: 1361-6404
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 43
• Issue: 1
• Article Number: 015803
• DOI: https://doi.org/10.1088/1361-6404/ac3671
• Public URL: https://durham-repository.worktribe.com/output/1216082