Analysis of Benford's Law Conformity with Web of Science Citations of Documents

Background: Benford's law is a statistical phenomenon that predicts the probability of a particular digit at a particular position in a number. This law has been successfully applied in a number of areas, such as accounting. In the area of scientometrics, research has been devoted mostly to journal data.Objective: This paper investigates the conformity of Benford's law with the citation counts of records retrieved from the Web of Science database. We evaluate the conformity levels with Benford's law in the complete dataset. We determine the effect of document type (article, proceedings paper and review), year of publication (2014-2018) and Web of Science categories (254 categories) on the level of conformity of the citation counts with Benford's law.Methods: The dataset of this research contains over 8.47 million records. All available records from the Web of Science were downloaded, so this set is the entire population of data available at the time of download. The distributions of the first significant digits in the citation counts of these records are compared with Benford's law. Mean absolute deviation (MAD) recommended by Nigrini (2012) and sum of squared deviations (SSD) recommended by Kossovsky (2015) are used to categorize the similarity of the citation counts to Benford's law.Results: The entire dataset of this study shows marginal conformity according to both MAD and SSD intervals (with a MAD value of 0.1257 and an SSD value of 29.9; a lower value indicates a better agreement). The review document type shows a high level of conformity, while proceedings paper shows a lower level. We found significant differences in conformity between Web of Science categories.Conclusion: This study mapped the level of conformity of the citation counts with Benford's law in data from the Web of Science database. Further directions for possible research are suggested.