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Digits and Deviation - Benfords Law

In a tremendous final-year project, two Durham undergraduates apply data-analysis techniques taught as part of their Physics degree to another real world data set - house prices.

A recent paper “Using residual heat maps to visualise Benford's multi-digit law” applies data-analysis techniques (chi-squared analysis, hypothesis compliance testing, quantitative analysis of differences between data and models) that are taught as part of a physics degree to another real world data set – house prices.

The paper can be found here:

The authors are two Durham physics undergraduate (Alexander Long and Benjamin Hull) supervised by Prof. Ifan Hughes of the QLM research group.

It has been known for more than a century that the frequency of occurrence of the first significant digit in a very large number of numerical data sets is nonuniformly distributed. This is Benford's law, which states that the first digit 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 Benford analysis was applied to the distribution of house prices in England and Wales pre and post-2014. A residual heat map analysis offers a visually attractive method for identifying interesting features.

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.

The data show a preference for prices finishing in 49 and 99 – hence the humorous attempts to introduce a 99p coin to reduce the need for small change!

Congratulations Alex and Ben for a tremendous final—year project conducted during lockdown.