The power of one : Benford's law

Abstract

The concept of Benford’s law, also known as the first-digit phenomenon, has been known to mathematicians since 1881. It is counter-intuitive, difficult to explain in simple terms, and has suffered from being described variously as ‘a numerical aberration’, ‘an oddity’, ‘a mystery’ – but also as ‘a mathematical gem’. However, it has developed into a recognised statistical technique with several practical applications, of which the most notable is as a fraud detection mechanism in forensic accounting. This paper will briefly discuss and demonstrate the special numerical characteristics of Benford’s law. It will attempt to investigate the law’s possible application to the detection of data manipulation and data tampering that might exist in papers published in engineering and scientific journals. Firstly, it will be applied to an investigation of the so-called Fisher-Mendel controversy. Secondly, Benford’s analysis will be applied to six recently published papers selected from the South African Journal of Industrial Engineering.

Die konsep van Benford se wet, ook bekend as die eerste-syfer-fenomeen, is bekend aan wiskundiges sedert 1881. Dit is teen-intuïtief, moeilik om te verduidelik op ’n eenvoudige wyse, en gaan gebuk onder verskeie beskrywings soos ‘’n numeriese afwyking’, ‘’n koddigheid’, ‘’n misterie’, maar ook as ‘’n wiskundige juweel’. Dit het nietemin ontwikkel in ’n erkende statistiese tegniek met vele praktiese toepassings, waarvan die gebruik as ’n bedrog betrappingsmeganisme in forensiese rekeningkunde noemens-waardig is. Hierdie artikel sal die spesiale numeriese karakteristieke van Benford se wet bespreek en demonstreer. Dit sal die wet se moontlike gebruik om datamanipulering en -vervalsing wat mag bestaan in ingenieurs- en wetenskaplike publikasies te identifiseer. Eerstens sal dit toegepas word om die sogenaamde Fisher-Mendel kontroversie te ondersoek. Tweedens sal dit gebruik word om ses artikels wat onlangs gepubliseer is in die Suid-Afrikaanse Tydskrif vir Bedryfsingenieurwese aan ’n Benford analise te onderwerp.