Benford’s Law offers a powerful, data-driven approach to anomaly detection. Discovered 150 years ago, it wasn’t until the 1990s that auditors began harnessing its potential for identifying irregularities in financial data. Today, the Benford’s Law community spans a wide range of professions and academic disciplines.
Benford’s Law offers a powerful, data-driven approach to anomaly detection. Discovered 150 years ago, it wasn’t until the 1990s that auditors began harnessing its potential for identifying irregularities in financial data. Today, the Benford’s Law community spans a wide range of professions and academic disciplines.
This book provides the latest research-based techniques packaged for ready usage by auditors and audit analytics professionals. Discover how to use Benford’s Law in continuous monitoring and pinpoint non-compliant vendors, accounts or other groups. Visual examples demonstrate how to identify and interpret the most common patterns Benford’s Law surfaces.
Auditors and assurance professionals will benefit from clear, practical explanations of advanced methods, making it easier to integrate these techniques into their workflows. Meanwhile, analytics and quantitative experts will find a rich toolkit of new techniques to enhance their capabilities. Whether you’re new to Benford’s Law or looking to deepen your expertise, this book equips you with the tools to transform how you detect anomalies in data.
Preface. Fundamentals: Non-Statistical Approaches to Benford's Law. 1.0
The Story of Benford's Law. 1.1 Setting Expectations. 1.2 What Does it Mean
to "Pass" or "Fail" Benford's Law?. 2.0 The Basics of Benford's Law. 2.1 The
First Significant Digit. 2.2 Benford's Law. 2.3 Testing Data. 2.4 Exceptions
to Benford's Law. 3.0 Common Results - with Graphs. 3.1 The Classic Example:
Avoiding a Limit. 3.2 Missing Data. 3.3 Spikes & Potential Duplicate
Transactions. 3.4 Imprecise or Estimated Data. 3.5 Data with Limits. 3.6 Not
Enough Data. 4.0 Intermediate Topics. 4.1 Two-Digit Test. 4.2 Example
Application: Greenhouse Gas Emissions. 4.3 Second Order Test. 4.4 Example
Application: Fleet Mileage. 4.5 Changing Scales. 4.6 Data Transformation. 4.7
Example Application: Accounts Payable Amounts. 4.8 Generating Random
Benford's Law-compliant Data. Advanced Techniques: Statistical Approaches to
Benford's Law. 5.0 Goodness-of-Fit Scores. 5.1 The D-(Distance) Score. 5.2
MAD (Mean Absolute Deviation). 5.3 Honorable Mentions: Chi-Squared and Other
Scores from the Math Department. 5.4 Last Place: The Z-Score. 6.0
Benford-like Distribution. 6.1 The Generalized Benford's Law. 6.2 Example
Application: Inventory Adjustments. 7.0 Finding High-Risk Groups. 7.1
Approach to Identifying High Risk Groups. 7.2 Example Application: FinCEN
Files. 8.0 Time Series Applications. 8.1 Binned Data. 8.2 Example
Application: Journal Entries. 8.3 Windowed Data. 8.4 Example Application: Law
Enforcement Gun Usage. 9.0 Benford's Law and Machine Learning. 9.1 Data
Quality Monitoring. 9.2 Benford's Law as a Feature. 9.3 Benford's Law as an
Outcome Variable. 9.4 Benford's Law for Evaluating ML/AI Models. 10.0 Beyond
Base
10. 10.1 The Benford's Law Formula in Other Bases. 10.2 The Concept of
Base Invariance. 10.3 Example Application - Determining the Base of a
Dataset. 10.1 Example of Base Invariance. Wrapping Up. 11.0 Professional
Practice and Benford's Law. 11.1 Benford's Law Throughout the Audit Process.
11.2 Professional Standards. 11.3 Special Notes on Fraud. 12.0 Case Study: IT
Incident Management. 12.1 Audit Background. 12.2 Data Preparation. 12.3
Implementing Benford's Law. 12.4 Analysis and Results. 12.5 Wrapping Up. 13.0
Advanced Case Study. 13.1 Audit Background. 13.2 Optimizing Benford's Law.
13.3 Benford's Law in Power BI. 13.4 Finding High Risk Groups. 13.5 Time
Series & Continuous Monitoring. 13.6 Wrapping Up. Appendices: Deriving
Benford's Law. A.1 Algebraic Approach. A.2 Visual Approach.
Daniel J. McCarville is a recognized audit analytics professional, researcher, and speaker with more than a decade of experience developing advanced tools for auditors and compliance teams. He currently leads the audit analytics team at an S&P 500 insurance firm. His statistical expertise spans Benfords Law, machine learning, and simulation, which he applies to detect anomalies and strengthen decision-making.
His peer-reviewed research has introduced novel applications of Benfords Law and new methods for identifying irregularities in standardized test data. He has published in Emerald Open Research and received the National Legislative Program Evaluation Societys Impact Award multiple times.
Daniel has presented at major professional conferences, including IIA events, and frequently speaks at universities to inspire the next generation of data professionals. He holds a masters degree in political science from the University of Kansas, as well as Data Science from Eastern University. He also holds CIA and CRMA designations from the Institute of Internal Auditors and DASM certification from the Project Management Institute.
