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Hull, B, Long, A and Hughes, IG (2022)

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

European Journal of Physics 43, 015803.

ISSN/ISBN: Not available at this time. DOI: 10.1088/1361-6404/ac3671

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.

@article{, doi = {10.1088/1361-6404/ac3671}, url = {}, year = 2022, publisher = {{IOP} Publishing}, volume = {43}, number = {1}, pages = {015803}, author = {Benjamin Hull and Alexander Long and Ifan G Hughes}, title = {Using residual heat maps to visualise Benford's multi-digit law}, journal = {European Journal of Physics}, }

Reference Type: Journal Article

Subject Area(s): Accounting, Economics