Zipf’s law identifies the frequency with which words appear in the English language. It may provide a baseline for auditors looking for suspicious words or phrases. If Zipf’s law was proven to work, would it work in other languages, such as Spanish?
In the business world, CEO letters, memos, workpapers, 10-Ks, tax forms, and other documentation are routinely produced, distributed, filled out, and read. Mistakes and errors are bound to happen, but what if something much larger, like fraud, is at play? Can companies reduce fraud by simply looking at the words on paper or on a screen? What if there were a way to detect repeated or suspicious words? Maybe this is where Zipf’s Law can play a role.
Zipf’s Law identifies the frequency with which words appear in the English language.1 The application of Zipf’s Law to documentation data may enable the detection of abnormal or potentially fraudulent words or phrases. It has the potential to help with the analysis of financial documentation for word frequencies or patterns. As we enter a new technological era, auditors will need new methods to review large volumes of transactions, datasets, and formal written documents for fraudulent activity. Zipf’s Law may provide a baseline for auditors, with suspicious words or phrases highlighting areas for further examination.
And if Zipf’s Law were proven to work in the English language, will it be capable of working in other languages, specifically Spanish?
A Look at Zipf’s Law
George Kingsley Zipf’s "Zipf's Law" sets the most frequently used word in English (“the”) with a rank of 1, and that it appears twice as often as a word ranked 2, and so on.2 Despite Zipf’s 1935 articulation of this phenomenon in English, there has been little research to determine if this law works with other languages.
The United States has economic relations with many countries in which there is a language barrier. Financial documents, CEO letters, and such all need to be translated into English for business in the United States.
As businesses become more complex and newer technologies, such as artificial intelligence, become embedded in business processes, internal and external fraud is at an all-time high. This poses a problem for auditors who need to adapt and use new methods for fraud detection. A quote from “An Investigation of Zipf's Law for Fraud Detection" states, “Proper data analysis is critical as a means of allowing auditors to streamline audit processes, bring fraudulent activities to light before they result in critical losses, minimize financial losses, and ensure compliance with business rules and external regulatory requirements.”3 Now more than ever, data analysis and information technologies are becoming an integral part of fraud detection and overall financial security.
Zipf’s Law may be able to help detect words or phrases that raise red flags. But it is important to note that Zipf’s Law has limitations. As the sample size increases, the law becomes increasingly less applicable.4 What this means is that a smaller sample size is required to measure effectiveness.5 This can be restrictive when analyzing data. Auditors must have a high level of assurance to prove statistical significance, and larger sample sizes are needed to achieve this. This seemingly limits Zipf’s Law’s ability to measure large quantities of data and increases its margin of error.
But Zipf’s Law’s limitation should not disqualify its use with other techniques. While Zipf’s Law measures the frequency of words, Benford’s Law, much more common in mathematical terms, measures the frequency of numerical data.6 Benford’s Law is more widely known and used, but numerical data in CEO letters, 10-Ks, memos, and so on only comprise a small percentage of what is recorded in financial documents. The majority of the documents are text rather than numerical. Zipf’s Law may only be useful in small sample sizes, but it filters data to a manageable size and word significance.
Currently, there are not many tests of the effectiveness of Zipf’s Law, but it may be able to help with anomaly detection.7
Zipf’s Law Meets the Spanish Language
Since proposing his theory, Zipf studied other languages, including German, Chinese, and French.8 Although Zipf studied other languages, he wrote nothing that addresses whether his law holds in other languages. Thus, there is little research about Zipf’s Law in the Spanish language and less in its use in detecting fraud.9
We took a look at a study published in PLoS ONE, which focused on Catalan, a language originating in Spain. This work delved into the sister language, Castilian, which the United States labels as “Spanish” and which our own work mainly focuses on.
Analysis of CEO Letters of Spanish Banks
We looked at five Spanish banks and ran tests on their CEO letters. We looked at Banco Cooperativo Español, Banco Santander, Banca March, Banco Sabadell, and Banco BVVA. The prompt we put into the AI engine was as follows: “Show a list of the top 50 most frequently used words, including filler words.” The results were interesting. The number-one-ranking word was "de," which translates to "of." Although more tests are needed to conclude that “de” is the number one word; among the five banks we looked at, “of” was the most frequent, which differs from English, where “the” is the top-rated word according to Zipf. The second-ranked word between the five banks switched between “el” and “la,” which translate to “the” in Spanish. If we were to follow Zipf’s Law’s properties, this would mean that “de” (“of”) appeared two times more than “el” or "la." In the test on Banca March, “de” appeared 142 times and “la” appeared 85 times. Banco Sabadell: “de” appeared 129 times and “el” 55 times. Banco BVVA: “de” appeared 158 times and “la” 74 times. Lastly, in Banco Cooperativo Español, “de” appeared 55 times and “el” 35 times. Banco Cooperativo Español appears as an outlier among the 5 banks, but further testing may be able to help us understand this difference.
What’s Next?
As businesses and technology grow, new methods of fraud detection need to improve as well. Methodologies that advance the study of Zipf’s Law in relation to fraud and its use in the Spanish language may be a fruitful path to determining its effectiveness. This is a niche topic and one in which there is not a lot of current information, let alone published data. However, we believe that through continuous research, we will be able to add to the data and help auditors and businesses gain insight into the intricacies of Zipf’s Law and its much-needed success in fraud detection.
1 "Zipf’s law," Encyclopedia Britannica.
2 Ibid.
3 Shi-Ming Huang, David C. Yen, Luen-Wei Yang, and Jing-Shiuan Hua, "An Investigation of Zipf's Law for Fraud Detection (DSS# 06-10-1826R (2))," Decision Support Systems 46, No. 1 (2008): 70-83.
4 David M. W. Powers, "Applications and Explanations of Zipf’s Law," New Methods in Language Processing and Computational Natural Language Learning (1998).
5 Mohamad Amin Pourhoseingholi, et al, “Sample Size Calculation in Medical Studies,” Gastroenterology and Hepatology from Bed to Bench, vol. 6,1 (2013): 14-7.
6 Adeola Odueke and George Weir, "Triage in Forensic Accounting Using Zipf's Law" (2012): 33-43.
7 Ibid.
8 Stanley S. Newman, American Speech 11, no. 2 (1936): 170–71.
9 N. Català, J. Baixeries, R. Ferrer-i-Cancho, L. Padró, A. Hernández-Fernández, “Zipf’s Laws of Meaning in Catalan,” PLoS ONE (Dec. 16, 2021).
Arly Hernandez is a graduate from Moravian University with a degree in accounting and a minor in Spanish. Mark Koscinski and Daniel O’Connor are associate professors of accounting practice at the Moravian University School of Business and Economics. They can be reached at koscinskim@moravian.edu and oconnord@moravian.edu, respectively.
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Statements of fact and opinion are the author's responsibility alone and do not imply an opinion on the part of the PICPA's officers or members. The information contained herein does not constitute accounting, legal, or professional advice. For actionable advice, you must engage or consult with a qualified professional.
