In: Knoth S, Schmid W, (Eds.) Vol. 14 (Frontiers in Statistical Quality Control). Cham: Springer, pp. 269-279.
ISSN/ISBN: Not available at this time. DOI: 10.1007/978-3-032-02975-1_14
Abstract: The Benford law is used worldwide for detecting nonconformance or data fraud of numerical data. It states that the significand of certain random variables is not uniformly but logarithmically distributed. Namely, the random first nonzero digit is equal to one with a probability approximately equal to 0.3. In this article, we consider data sets manipulated by multiple entries and are looking whether such data fraud may be detected by statistical tests of Benford's law. Therefore, we designed a scenario for simulating data manipulations based on duplicated values. We estimate the rejection probabilities of four goodness-of-fit tests, applied to the first and second significant digits: Pearson's $\chi$2{\$}{\$}{\backslash}chi ^2{\$}{\$}-test, a modified version of the mean absolute deviation test, and two invariant sum tests motivated by the invariant sum property of Benford's law and relying on the Euclidean and Mahalanobis distances. It turns out that in the majority of cases, the invariant sum tests outperform the remaining goodness-of-fit tests.
Bibtex:
@InProceedings{,
author="K{\"o}ssler, Wolfgang and Lenz, Hans-J.
and Wang, Xing D.",
editor="Knoth, Sven and Schmid, Wolfgang",
title="Detecting Manipulated Data Sets Using Benford's Law",
booktitle="Frontiers in Statistical Quality Control 14",
year="2026",
publisher="Springer Nature Switzerland",
address="Cham",
pages="269--279",
doi = "10.1007/978-3-032-02975-1_14",
isbn="978-3-032-02975-1"
}
Reference Type: Conference Paper
Subject Area(s): Statistics