Open AccessUsing residual heat maps to visualise Benford’s multi-digit law
Author(s) -
Benjamin P. Hull,
A.B. Long,
Ifan G. Hughes
Publication year - 2021
Publication title -
european journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.421
H-Index - 51
eISSN - 1361-6404
pISSN - 0143-0807
DOI - 10.1088/1361-6404/ac3671
Subject(s) - benford's law , residual , intuition , logarithm , econometrics , distribution (mathematics) , law , economics , physics , statistics , mathematics , mathematical analysis , algorithm , psychology , political science , cognitive science
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.