MAB-scriptieprijs

Benford’s Law and Beyond: A framework for auditors

Long Le^‡§, Eric Mantelaers ^§|¶#¤

‡ RSM NL, Hoofddorp, Netherlands

§ Maastricht University, Maastricht, Netherlands

| Zuyd University of Applied Sciences, Sittard, Netherlands

¶ RSM Netherlands Accountants N.V., Netherlands

# FHR Business School, Paramaribo, Suriname

¤ Nyenrode, Breukelen, Netherlands

Corresponding author: Long Le ( ledoanhlong3@gmail.com )

Academic editor: Ralph ter Hoeven

This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY-NC-ND 4.0), which permits to copy and distribute the article for non-commercial purposes, provided that the article is not altered or modified and the original author and source are credited.

Citation: Le L, Mantelaers E (2024) Benford’s Law and Beyond: A framework for auditors. Maandblad voor Accountancy en Bedrijfseconomie 98(7): 427-438. https://doi.org/10.5117/mab.98.134061

Abstract

We propose a systematic framework that integrates Benford’s Law – a mathematical principle predicting the frequency distribution of leading digits – with advanced statistical and machine learning techniques for enhanced anomaly detection in financial auditing, especially highlighting actionable next steps for implementation. This framework combines Benford’s Law with K-means clustering and multi-digit analysis (First-two and First-three digits) to effectively distinguish between errors, benign anomalies, and fraudulent activities. Empirical validation on financial transaction data demonstrates significant improvements in fraud detection accuracy and reliability, offering practical insights and guidance for auditors on adopting a more robust approach to anomaly detection in modern auditing practices.

Keywords

Benford’s Law, Fraud Detection, K-Mean Clustering, Multiple Digits Analyses, Financial Auditing

Relevance to practice

This framework equips auditors with an advanced toolset, integrating Benford’s Law with statistical and machine learning techniques to enhance anomaly detection accuracy. Beyond initial detection, it offers actionable insights and practical guidance, empowering auditors to reliably address financial irregularities and improve the precision of financial reporting.

1. Introduction

In today’s globalized economy, financial markets are crucial for capital flow, risk management, and supporting business operations. Yet, the increasing complexity of transactions and the massive data generated by digitized systems have made fraud detection and ensuring the accuracy of financial statements more challenging (AFM 2024). Integrity in financial reporting is vital for capital markets, corporate performance assessment, and maintaining stakeholder trust. Fraudulent activities like asset misappropriation, corruption, and financial statement fraud undermine this trust, with significant implications for businesses, investors, and the economy (IAASB 2024a; ISA 240).

As financial data becomes more complex, auditors need advanced tools for effective anomaly detection. Benford’s Law has emerged as a key tool, leveraging statistical principles to predict leading digit frequencies in naturally occurring datasets. In such datasets, the number 1 appears as the leading digit roughly 30% of the time – far more than the expected 11.1% if digits were uniformly distributed (Nigrini 2022). This makes Benford’s Law a valuable initial screening method in auditing, identifying anomalies that may signal errors or fraud in financial records.

However, detecting anomalies is only the first step. Auditors must determine whether deviations result from simple errors, like data entry mistakes, or more serious fraud. The increasing sophistication of fraud schemes requires a more refined approach to post-anomaly detection, as fraudsters find ways to manipulate data that conform to traditional models.

This paper aims to bridge the gap by developing a systematic framework for auditors to follow after identifying anomalies using Benford’s Law. By integrating advanced statistical and machine learning techniques like K-means clustering and multi-digit analysis, the framework aims to improve the accuracy of fraud detection. Despite the extensive use of Benford’s Law, there is limited guidance on subsequent investigative procedures. This article addresses this gap by providing auditors with a clear set of steps to distinguish between errors and fraud more accurately.

As the auditing profession evolves with technological advancements, integrating modern tools such as Benford’s Law into standard practices has become increasingly important (Mantelaers 2021). This research supports that effort, combining traditional methods with advanced anomaly detection techniques. With growing regulatory focus on fraud detection, such as from the Dutch Authority for Financial Markets (AFM 2024), auditors must adopt new tools to ensure accurate financial reporting. Thus, this study explores the research question:

“What auditing procedures should auditors perform after identifying possible anomalies using Benford’s Law?”

The paper is structured as follows: the introduction has outlined the role of Benford’s Law and the need for systematic post-detection procedures. The literature review in section 2 examines current methodologies, while the methodology section (section 3) details the approach used in this study. Section 4 (findings) and section 5 (discussion) present the results and analyze their implications for auditors. Section 6 (conclusion) summarizes key insights, discusses study limitations, and suggests future research directions.

By focusing on post-anomaly detection actions, this paper provides practical guidance and a robust framework to enhance the effectiveness of financial audits. It contributes to the field of fraud detection and anomaly analysis, offering a practical solution tailored to the complexities of today’s financial environment.

2. Literature review

2.1. Benford’s Law in auditing

Integrating Benford’s Law into auditing has significantly advanced the detection of anomalies and potential fraud. Auditors use Benford’s Law as a diagnostic tool to identify irregularities in financial records, such as income statements and balance sheets, which may suggest fraudulent activities or errors (Boffa 2023). Its predictive model of leading digit frequencies allows auditors to benchmark expected distributions, enabling the identification of deviations that warrant further analysis (Leonov et al. 2022b). Research shows that Benford’s Law effectively detects inconsistencies in financial data, helping uncover issues that might otherwise go unnoticed (Abdul Aris et al. 2015; Sylwestrzak 2023). However, distinguishing between errors and fraudulent anomalies remains a challenge. Errors typically result from unintentional mistakes like data entry or computational errors, while fraudulent anomalies suggest deliberate manipulation to deceive stakeholders (Arezzo and Cerqueti 2023; Zenkov 2021). Understanding this distinction is crucial for auditors, as it guides the depth and direction of investigations. For instance, errors may require simple corrections, whereas fraud necessitates thorough investigation and possible legal action (Sylwestrzak 2023). This study aims to address the challenge of distinguishing between errors and fraudulent anomalies flagged by Benford’s Law. When applying Benford’s Law, auditors assess whether a dataset conforms to expected digit distributions. If anomalies are detected, further statistical tests, like the Z-test or Mean Absolute Deviation (MAD), help determine their significance. Statistically significant deviations suggest issues beyond random chance, indicating a need for deeper investigation (Etim et al. 2023; Nigrini 2012). Conversely, non-significant deviations may be due to natural data variations and require less follow-up, though auditors should consider them within the broader audit context (Carmo et al. 2023). Using statistically significant criteria enhances the precision of Benford’s Law in detecting irregularities. Methods like the Z-test provide a systematic way to assess deviations, while also incorporating the auditor’s expertise for a holistic interpretation of results (Kowsher 2018). Conformity tests are valuable tools, but they are not definitive proof of fraud. They should be used alongside professional judgment and other investigative methods to strengthen the overall audit process.

2.2. Existing literature on beyond Benford

2.2.1. Further Benford’s tests (Second Digit, First-Two Digit, Last-Two Digit)

Beyond the First Leading Digit Test, Benford’s Law includes further methods like the Second-Digit Test, First-Two Digit Test, and Last-Two Digit Test, adding depth to anomaly detection (Nigrini 2012). These tests provide enhanced sensitivity by uncovering patterns that might escape the basic first-digit analysis. For example, the Second-Digit Test identifies irregularities that evade initial detection, offering a deeper layer of scrutiny (Nigrini 2012). The First-Two Digit Test can reveal duplicate transactions below material thresholds, indicating potential fraud (Aris et al. 2017). The Last-Two Digit Test helps identify rounding patterns, which could suggest manipulative behavior, such as rounding up earnings to meet targets (Das and Zhang 2003; Tran et al. 2023).

While these tests can detect subtle irregularities, they have limitations. The First-Two Digit Test requires large, diverse datasets and statistical expertise, which may challenge smaller audit practices (Cleary and Thibodeau 2005). Additionally, these methods can produce false positives, requiring careful interpretation to prevent unnecessary resource use. Although these advanced tests extend Benford’s scope, they often lack guidance on actions to take after identifying anomalies. This gap underscores the need for research that combines sophisticated detection methods with practical auditing strategies.

2.2.2. Audit sampling

The International Auditing and Assurance Standards Board (IAASB 2024b; ISA 520) supports using statistical or non-statistical sampling for detailed audit testing. Antonio (2023) demonstrated this by auditing a random 10% sample of transactions identified as anomalies using Benford’s Law, finding both human errors and misappropriation. Da Silva and Carreira (2013) proposed models for audit sampling based on Benford’s Law to identify nonconforming records. However, Benford’s Law assumes that datasets naturally conform to its expected digit distributions, which is not always true for restricted or manipulated data, such as tax rates or pricing strategies (Leonov et al. 2022a; Nigrini 2012). Additionally, Benford’s Law may miss anomalies that do not affect leading digit distributions, potentially overlooking critical issues (Durtschi and Pacini 2004). These challenges highlight the importance of using Benford’s Law alongside other sampling methods and qualitative analyses for a comprehensive audit.

2.2.3. Machine learning

Machine learning (ML) and artificial intelligence (AI) have significantly expanded the scope of anomaly detection in auditing. Bhattacharya et al. (2011) combined Benford’s Law with neural networks to create classifiers that differentiate between fraudulent and error-prone anomalies. Badal-Valero et al. (2018) demonstrated how logistic regression and support vector machines could identify high-risk areas by analyzing patterns beyond Benford’s scope. While ML enhances detection, it lacks the contextual understanding needed for follow-up actions, relying on training data without deeper insight into anomalies (Sifa et al. 2019).

Challenges in using ML for fraud detection include training data imbalances, where fraudulent cases are far fewer than legitimate transactions, leading to less accurate models (Badal-Valero et al. 2018; Sylwestrzak 2023). Furthermore, ML tools often rely on pre-labeled fraudulent cases, a condition rarely matched in real-world audits. This can limit their practical application in audits, where uncertainty is common. The high costs of false positives, such as unnecessary investigations, further highlight the need for ML tools to be complemented with human expertise and additional analyses to ensure balanced and effective audit decisions (Beneish and Vorst 2022).

2.2.4. Others

Amiram et al. (2015) introduced the Financial Statement Divergence (FSD) score, which leverages Benford’s Law to assess deviations in financial statements, serving as a reliability indicator. The FSD score can predict material misstatements and act as an early warning signal. However, Walker (2022) found the FSD score less effective when used alone for detecting major errors and highlighted that adding the F-score showed mixed results in predictive accuracy. Cano‐Rodríguez et al. (2023) also questioned the reliability of the FSD score.

Tammaru and Alver (2016) developed a simpler version of the FSD score to detect earnings management by comparing expected and actual item counts. This method has been applied to assess financial credibility (Leonov et al. 2022b). Chakrabarty et al. (2024) recently introduced the AB-score and ABF-score, combining Benford’s Law with the F-score model. These metrics outperform traditional models like support vector machines, offering higher accuracy in fraud detection. The ABF-score is particularly effective in reducing false positives and negatives, thus improving audit precision. While the integration of Benford’s Law with machine learning in the ABF-score offers advanced fraud detection capabilities, its effectiveness can be constrained by limited training datasets with insufficient fraud cases.

2.3. Gap in literature

Despite the widespread use of Benford’s Law for anomaly detection in auditing, significant gaps remain in guiding auditors on subsequent investigative procedures and integrating advanced analytical tools (Anderson et al. 2022). While Benford’s Law effectively screens for irregularities, standardized protocols for post-detection investigations are notably lacking. This absence underscores the need for frameworks that guide auditors through the process of distinguishing errors from fraud and resolving anomalies. Additionally, there is limited empirical research on combining Benford’s Law with modern technologies like machine learning, which could greatly enhance fraud detection accuracy (Mumic and Filzmoser 2021). Current studies often address these advanced tools separately, missing the opportunity to explore their integrated application in auditing (Kowsher 2018).

Auditors’ methods range from traditional manual audits to complex machine learning techniques (Renaldo et al. 2022; Sylwestrzak 2023). Manual audits, though rooted in standard practices, often struggle with the complexity of modern financial datasets, potentially missing subtle indicators of fraud (Etim et al. 2023). These methods can be time-consuming and costly, with high resource demands (Buchner 2022). On the other end, machine learning offers greater precision and the ability to process large data volumes (Badal-Valero et al. 2018), but it comes with significant costs and requires specialized expertise, making it less accessible for smaller audit firms. The literature highlights the need for a balanced approach – one that combines the strengths of both traditional and advanced methods without excessive costs.

The analysis of existing research emphasizes Benford’s Law’s potential as a cost-effective and versatile tool for detecting irregularities across various datasets. Yet, there is no consensus on best practices for investigating anomalies post-detection, with significant variation across studies. This highlights the need for standardized guidelines that align with the complexities of modern financial systems. Furthermore, a lack of empirical studies confirming the synergy of advanced statistical and machine learning tools with Benford’s Law limits their practical application. A multidisciplinary approach that integrates these advanced methods with traditional auditing practices could significantly improve auditors’ ability to differentiate between benign anomalies, errors, and fraud.

This research seeks to address these gaps by developing a systematic framework for auditors to follow after detecting anomalies using Benford’s Law. By combining empirical validation with the integration of advanced technologies and conventional methods, the study aims to enhance both audit quality and financial reporting reliability. The findings have practical implications for audit practices, offering a foundation for a more refined approach to fraud detection and setting a new standard for anomaly detection in financial audits.

3. Methodology

3.1. Conceptual Framework

This paper aims to develop a framework to assist auditors beyond the anomaly’s detection of Benford’s Law. The independent variable “Benford’s Law” is analyzed on how it will affect the dependent variable, “Potential Fraud Detection” with the moderator being “Types of Analysis”. The conceptual framework can be seen in Figure 1.

Figure 2.

Research procedures.

3.2. Techniques and procedures

Figure 2 summarizes the research techniques and procedures of this paper.

Figure 1.

Research Framework.

3.2.1. K-Mean Clustering

According to Nonnenmacher and Gómez (2021), dividing the initial data into subsets (clustering) can mitigate data quality issues. Therefore, a greater amount of information could be acquired that would not have been obtained had the data not been divided into subsets. Dividing data into subsets before applying Benford’s Law significantly enhances the precision and relevance of anomaly detection in auditing processes (Anderson et al. 2022). This methodological approach allows for a more targeted analysis, isolating specific segments of data that may exhibit distinct financial behaviors or characteristics that could be obscured in a comprehensive dataset analysis. By analyzing these subsets, auditors can identify nuanced patterns of irregularities that are tailored to different operational areas or transaction types, enabling a more focused and effective investigation. Furthermore, this segmentation facilitates the identification of localized issues within the data, potentially leading to more accurate diagnostics and efficient resolution of anomalies (Smith 2017). This strategic partitioning not only increases the granularity of the analysis but also improves the overall utility of Benford’s Law in practical auditing scenarios, making it a vital tool for auditors seeking to enhance the accuracy and efficiency of their work.

3.2.2. Testing for Benford’s Law

One of the most common tests to see if a dataset is conformed to Benford’s Law is the Chi-square test due to its robustness in analyzing distribution of data (Cerqueti et al. 2021). However, it has recently been proven by Kossovsky (2021) that the Chi-square test is often unsuitable for assessing conformity to Benford’s Law because it not only evaluates the distribution of leading digits but also assumes that the dataset represents a random sample from a defined population. However, Benford’s Law typically applies to non-random datasets such as financial records or election results, where all entries are analyzed without selection. Using the Chi-square test can lead to misleading conclusions, falsely attributing non-conformity to the randomness of data collection rather than to actual deviations in digit frequencies. Therefore, alternative statistical measures that directly assess the fit to Benford’s distribution, without assuming data randomness, are preferable for such analyses (Kossovsky 2021). Therefore, this paper will use the Z-Statistic and the Mean Absolute Deviation test to test conformity to Benford’s Law.

3.3 Further Digit Analyses

First-Two-Digits Test: this test is a refined tool for auditors following initial anomalies detected with Benford’s Law, particularly when deviations involve specific starting digits, such as ‘4’. Aris et al. (2017) and Nigrini (2012) note its effectiveness in identifying potential fraud, such as duplicate transactions or those strategically placed just below review thresholds. For example, if the review threshold is 5,000, a cluster of transactions starting with ‘49’ might suggest an attempt to evade detection while cumulatively concealing significant manipulation. This test helps auditors spot subtle yet telling patterns of irregularities.

First-Three-Digits Test: extending the First-Two-Digits analysis, the First-Three-Digits test delves deeper into transactional data to uncover finer details of potential manipulation (Aris et al. 2017). This approach is especially valuable when initial findings suggest fraud but lack detailed evidence. By analyzing the first three digits, auditors can detect duplicate transactions sharing a common prefix, such as ‘495’, which could indicate systematic fraud if these transactions frequently fall near a financial threshold (Smith 2017). This additional layer of detail helps identify patterns that might be missed in less granular analyses, providing a more comprehensive view of potential fraud.

4. Results

77 datasets of financial transactions were analyzed using Benford’s Law First Digit. Of which only 36 datasets satisfy the Benford’s requirements:

Have a large sample size, with a minimum of 5.000 entries.
The numbers must arise naturally and should not have imposed minimums or maximums.
The dataset should span several orders of magnitude.
The leading digits should not be constrained by the process generating the numbers.
The data collection should be unbiased and avoid systematic influences on the first digit.

This paper will show the detailed analysis of 3 financial datasets:

One follows Benford’s Law perfectly (Dataset 1)
One with anomalies significantly higher than expected (Dataset 2)
One with anomalies significantly lower than expected (Dataset 3)

These datasets contained financial transactions of the above-mentioned companies (dataset 1, dataset 2 and dataset 3). As a part of the data cleaning process, all the transactions starting with 0 such as 0,5; 0,99; etc. were removed. They were not rounded up to 1 since it will skew the distribution. Furthermore, all the transactions were taken at absolute value, meaning that all the negative values (credit entries) are ignored (Nigrini 2022). Table 1 summarizes the findings of the research.

Table 1.

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Summary of research’s finding.

Dataset	Possible anomalies
Dataset 1 (Perfect Dataset)	40 (Small)
	50 (Small)
	100 (Medium)
	103 (High)
Dataset 2 (Higher)	100
Dataset 3 (Lower)	499

Initially, dataset 1 appeared to follow Benford’s Law. However, as we divided the dataset into 3 subsets using K-Mean Clustering, statistically significant deviations were found in each subset. In contrast, the dataset for Client B revealed a substantial number of deviations from the expected Benford distribution. Both the Z-test and MAD test identified significant irregularities, with certain digits, particularly those starting with ‘1’. Using the First-Two and First-Three Digit Tests, it was found that this was cost by a large amount of transaction starting with figure 100. This is the same case for dataset 3 with figure 499. For more detailed analysis, see the Appendix 1.

5. Discussions

5.1. Result validation

Manual audit was performed by an auditor by examining the transactions closely to validate the finding of this research. For dataset 2, out of 664 transactions starting with 100, 604 of them were transactions with value 100. Among those 604 transactions, 310 of them were labelled: “Inhouding eigen bijdrage auto”, meaning “Deduction of personal contribution for car” and 236 of them were labelled: “Netto vergoeding”, meaning: “Net compensation”. These 2 types of transaction combined make up the majority of transactions with a value of 100 and is the reason why digit 100 is significantly higher than expected. The auditor confirmed that these transactions are not fraudulent since the company in questioned deducted 100 euros from every employee’s yearly salary as a part of personal contribution to company’s cars and some employees are then compensated these 100 euros back. This explains why there are so many transactions starting with 100, since the company has to do this for every single employee.

For dataset 3, out of 516 transactions starting with 499, 442 of them were transactions with value 499. Among those 442 transactions, 164 of them were labelled: “Betalingen via iDEAL”, meaning “Payment by IDEAL”, and 198 of them were labelled: “Geld Onderweg”, meaning “Money on the way”. These 2 types of transaction combined make up most of transactions with a value of 499, and is the reason why digit 499 is significantly higher than expected. However, the auditor also confirmed that these transactions are not fraudulent since the company in questioned sell a lot of products online which have a price of 499. They seem to sell a lot of this products and most of the payment were made by cards, which explains why there are so many transactions with the value of 499 labelled “Payment via Ideal” and “Money on the way”.

For dataset 1, the result was inconclusive with just examining the transactions and the auditor did not have enough time to conduct a full manual audit. Therefore, further investigation is needed for those anomalies (IAASB 2024a; ISA 240). These include conducting an interview with the managers as well as the responsible employees to gather explanations and understand the context. They may ask about the processes and controls in place to identify any weaknesses or lapses that could have led to the anomalies. The auditors could also look for patterns between these anomalies, for example, all the anomalies of Client 1 came from bank account transactions and are mostly related to credit cards. Furthermore, auditors must cross-check with other data by comparing the flagged transactions with data from other sources (e.g., bank statements, supplier invoices) to ensure consistency (IAASB 2024b; ISA 520). Table 2 summarizes the validation of the findings.

Table 2.

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Result validation from the auditor.

Dataset	Possible anomalies	Validation
Client 1 (Perfect Dataset)	40 (Small)	Inconclusive, further audit needed
	50 (Small)
	100 (Medium)
	103 (High)
Client 2 (Higher)	100	Not Fraud
Client 3 (Lower)	499	Not Fraud

5.2. Future framework for auditors

Figure 3 shows a potential framework for auditors on what to do beyond Benford’s Law.

The process of sub-setting the data before applying Benford’s Law can help us reveal new insights that were hidden. However, the segmentation of the dataset into three subsets: small, medium and high is tricky and can be time consuming. Therefore, it should only be done when the dataset seems to follow Benford’s Law perfectly. If there is a significant deviation between Benford’s law and the actual data, then the further digit tests (First-Two and First-Three) are enough to significantly reduce the manual audit sample size. After the audit sample size has been determined, a detailed manual audit must be done. The procedures include interviewing the managers and employees responsible for the transactions, looking for patterns in the anomalies and examine the transactions carefully. This provides an answer to our main research question: “What auditing procedures should auditors perform after identifying possible anomalies using Benford’s Law?”

Figure 3.

Potential audit framework for auditors beyond Benford’s Law.

5.3. Audit program for auditors

Based on the framework suggested in Figure 3, an audit program that will help auditors to detect anomalies using Benford’s Law is outlined below:

Step 1: Audit planning

Objective: Define the scope and objectives of the audit.
Understand the business, its environment, and identify the key areas of risks
Establish materiality thresholds.

Step 2: Data preparation and initial analysis

Objective: Prepare the dataset for Benford’s Law analysis.
Obtain the financial dataset.
Clean the data by removing non-numeric entries, removing transactions starting with 0 and ensuring all transactions are absolute values.
Check if the dataset meets the requirements for Benford’s Law (e.g., minimum of 5,000 records, naturally occurring numbers, spanning several orders of magnitude).

Step 3: Benford’s Law analysis

Objective: Detect anomalies in the dataset using Benford’s Law.
Apply Benford’s Law to the entire dataset.
Calculate the expected and observed frequency distributions of leading digits.
Perform the Z-Test and Mean Absolute Deviation (MAD) test to assess conformity.
The MAD test to access the conformity to Benford’s Law of the whole dataset.
The Z-Test to access the conformity to Benford’s Law of the individual digit.
Identify significant deviations from the expected distribution.
If the data follows Benford’s Law and no significant deviation is found, go to Step 4.
If the data does not follow Benford’s Law and significant deviation is found, go to step 5.

Step 4: Data segmentation

Objective: Enhance the precision of anomaly detection by segmenting the data.
Segment the dataset using K-means clustering into small, medium, and high-value transactions.
Reapply Benford’s Law analysis to each segment.
Calculate Z-scores and the MAD for each subset to identify statistically significant anomalies.

Step 5: Multiple digit tests

Objective: To further investigate the significant anomalies and narrow down the audit sample size.
Perform First-Two Digit tests(10 to 99) on each segment or the entire dataset
Perform First-Three Digit tests (100 to 999) on each segment or the entire dataset
Calculate Z-scores and the MAD for each subset to identify statistically significant anomalies.

Step 6: Investigation of anomalies

Objective: Determine the nature of detected anomalies.
Investigate high-deviation digits in each segment.
Conduct a manual audit on transactions starting with digits showing significant deviations.
Manual audit procedures include an interview with the managers and responsible employees, detailed examination of the suspicious transactions, etc.
Conclude the Manual Audit

Step 7: Audit documentation

Objective: Ensure all audit work is properly documented.
Maintain detailed workpapers for all analyses and findings.
Document findings, conclusions, and recommendations.
Ensure audit files are complete and organized.

Step 8: Audit reporting

Objective: Communicate audit findings to stakeholders.
Prepare the draft audit report.
Discuss findings with management.
Finalize and issue the audit report.
Present findings to the audit committee or board of directors.

Step 9: Follow-up

Objective: Ensure that corrective actions are taken.
Monitor implementation of recommendations.
Conduct follow-up audits if necessary.

5.4. Limitations and future research

5.4.1. Limitations

Despite the substantial discoveries and contributions of this research, it is essential to point out several limitations. First, the applicability of Benford’s Law necessitates that datasets satisfy specific criteria, including size, natural occurrence, and diversity. The generalizability of the findings to other types of financial data that do not inherently conform to Benford’s Law may be restricted by the fact that this study exclusively examined datasets that met these criteria. Additionally, although effort was made to ensure that only datasets of sufficient size were chosen, certain subsets may still be affected by the limited sample sizes, particularly when they are divided into smaller groups. This has the potential to impact the reliability and robustness of anomaly detection results. Finally, the auditor’s judgment remains a significant factor in the interpretation of anomalies. Although statistical tools serve as a foundation for identifying potential issues, the ultimate determination of fraud versus error demands an in-depth understanding of the context, which can differ significantly among auditors.

5.4.2. Future research

Building on the findings of this study, future research could further investigate the combination of K-Means Clustering with Benford’s Law. The results from this study showed that dividing data into clusters and applying Benford’s Law significantly improved fraud detection accuracy. Future studies could explore other clustering algorithms and their impact on fraud detection efficiency. Furthermore, the datasets used in this paper did not contain fraudulent data. Therefore, future research could use the research framework proposed by this paper and apply it to data that contained fraudulent data to validate the accuracy and reliability of the algorithms.

In addition, future study could extend this model to include the Last-Two Digit test. The Last-Two- Digits test is particularly valuable for identifying falsifications related to financial rounding or the creation of fictitious numbers (Aris et al. 2017). Often used to scrutinize the integrity of financial records, this test examines whether the endings of transaction figures suggest unnatural patterns. In retail settings or industries where pricing strategies typically end prices in ‘.99’ or ‘.95’, a disproportionate number of transactions ending in ‘00’ might indicate that numbers have been rounded up or entirely fabricated. Such findings could suggest the presence of fraudulent activities, especially if these rounded transactions cluster within certain departments or are frequently authorized by specific individuals, providing a lead for further investigation.

6. Conclusion

The integration of Benford’s Law into auditing practices, as explored in this article, underscores its potential as a powerful tool for anomaly detection in financial datasets. This research not only reaffirms the utility of Benford’s Law in identifying irregularities but also addresses a critical gap in the literature by proposing a systematic framework for post-detection auditing procedures. The empirical validation of this framework, through case studies and advanced statistical methods such as K-mean clustering, demonstrates its efficacy in distinguishing between benign anomalies and potential fraud. Moreover, the incorporation of machine learning techniques alongside traditional auditing methods enhances the precision and reliability of fraud detection, offering a robust toolkit for auditors. This multidisciplinary approach, blending insights from forensic accounting, data science, and risk management, represents a significant advancement in auditing methodologies. By providing actionable guidelines for auditors, this paper contributes to the enhancement of audit quality and the integrity of financial reporting. Future research should continue to explore the integration of emerging technologies to further refine and validate these procedures, ensuring their adaptability to the evolving landscape of financial fraud and complexity of modern financial systems.

L. Le – Long ¹ is a Technology Consultant at RSM Netherlands. He recently graduated from Maastricht University with a master degree in Business Intelligence and Smart Services.

Dr. E.J.H.J. Mantelaers RA AA CFE CISA C|CISO – Eric is a partner at the Center of Digital Innovation (CODI) of RSM Netherlands. He is also a professor of applied sciences at the Future-proof Auditor research group of Zuyd University of Applied Sciences and a senior lecturer in the Audit & Assurance program at Maastricht University. At Erasmus University, Eric is affiliated with the Executive Program Financial Forensic Expert.

Note

This article is based on Long Le’s master thesis. This makes him one of the winners of the MAB Thesis Award 2024.

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