Statistical Forensics

Checking the Distribution of Rightmost Digits

General Information

One technique that can be used to detect scientific misconduct is to check the rightmost digits of the data collected. Recorded numbers in each study should be unrepeatable, if there are any patterns, then there is reason for suspicion. For example, when running through a program multiple times you see that numbers continuously end in a ‘6’ or a ‘2,’ then one may want to double check the data collected because these numbers should not continuously end in the same two numbers in high ratios. Read about Checking for Rightmost Numbers by checking out the links below. 

Here are some resources on the technique:

Beber, B., Scacco, A., & Alvarez, R. M. (2012). What the numbers say: A digit-based test for election fraud. Political Analysis, 211-234.

Benford, F. (1938) The Law of Anomalous Numbers. Proceedings of the American philosophical society, 551-572.

Check Rightmost Digits for Uniform Distribution. The Office of Research Integrity

Diekmann, A. (2007). Not the First Digit! Using Benford’s Law to Detect Fraudulent Scientific Data. Journal of Applied Statistics, 34(3), 321-329.

Dlugosz, S., & Müller-Funk, U. (2009). The value of the last digit: statistical fraud detection with digit analysis. Advances in data analysis and classification, 3(3), 281-290.

Kossovsky, A. E. (2012). Statistician’s New Role as a Detective – Testing Data for Fraud. Ciencias Económicas 30(2).

Mosimann, J., Dahlberg, J ., Davidian, N., & Krueger, J. (2002). Terminal digits and the examination of questioned data. Accountability in Research: Policies and Quality Assurance, 9(2), 75-92.445.

Nigrini M. J., & Mittermaier L. J. The use of Benford’s law as an aid in analytical procedures. Auditing. 1997;16(2):52-67. 

Pitt, J. H., & Hill, H. Z. Statistical Detection of Potentially Fabricated Numerical Data: A Case Study.

Preece, D. (1981). Distributions of Final Digits in Data. Journal of the Royal Statistical Society. Series D (The Statistician), 30(1), 31-60. doi:10.2307/2987702

Using Benford’s Law to Detect Fraud. (2018). Association of Certified Fraud Examiners.

Walter, C. F. & Richards III, E. P. Legal Defenses to the Use of Data Digits to Identify Fabricated Data. The Climate Change and Public Health Law Site.