, Volume 88, Issue 2, pp 421–432 | Cite as

Benford’s law and citations, articles and impact factors of scientific journals

  • Juan Miguel CampanarioEmail author
  • María Angeles Coslado


First order digits in data sets of natural and social data often follow a distribution called Benford’s law. We studied the number of articles published, citations received and impact factors of all journals indexed in the Science Citation Index from 1998 to 2007. We tested their compliance with Benford’s law. Citations data followed Benford’s law remarkably well in all years studied. However, for the data on the numbers of articles, the differences between the values predicted by Benford’s law and the observed values were always statistically significant. This was also the case for most data for impact factors.


Benford law Citations Articles Impact factor 



This research was supported in part by a grant from the Spanish Ministry of Science and Technology (Dirección General de Investigación) and the European Regional Development Fund (ERDF/FEDER, project SEJ2007-66236/SOCI). We thank K. Shashok for improving the use of English in the manuscript.


  1. Benford, F. (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, 78, 551–572.Google Scholar
  2. Cohen, D. (1976). An explanation of first digit phenomenon. Journal of Combinatorial Theory Series A, 20, 367–370.zbMATHCrossRefMathSciNetGoogle Scholar
  3. Gauvrit, N., & Delahaye, J. P. (2008). A new general explanation of Bendford’s law. Mathematics and Social Sciences, 182, 7–15.zbMATHMathSciNetGoogle Scholar
  4. Hales, D. N., Sridharan, V., Radhakrishnan, A., Chakravorty, S. S., & Siha, S. M. (2008). Testing the accuracy of employee-reported data: An inexpensive alternative approach to traditional methods. European Journal of Operational Research, 189, 583–593.zbMATHCrossRefGoogle Scholar
  5. Jolion, J. M. (2001). Images and Benford’s Law. Journal of Mathematical Imaging and Vision, 14, 73–81.zbMATHCrossRefMathSciNetGoogle Scholar
  6. Judge, G., & Schechter, L. (2009). Detecting problems in survey data using Benford’s law. Journal of Human Resources, 44, 1–24.Google Scholar
  7. Kumar, K., & Bhattacharya, S. (2002). Benford’s law and its application in financial fraud detection. Advances in Financial Planning and Forecasting, 11, 57–70.CrossRefGoogle Scholar
  8. Newcomb, S. (1881). Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics, 4, 39–40.CrossRefMathSciNetGoogle Scholar
  9. Ni, D. D., Wei, L., & REN, Z. Z. (2009). Benford’s Law and β-decay half-lives. Communications in Theoretical Physics, 51, 713–716.CrossRefGoogle Scholar
  10. Pain, J. C. (2008). Benford’s law and complex atomic spectra. Physical Review E, 77, 012008–012102.CrossRefGoogle Scholar
  11. Shao, L., & Ma, B. Q. (2009). First digit distribution of hadron full width. Modern Physics Letters A, 24, 3275–3282.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  • Juan Miguel Campanario
    • 1
    Email author
  • María Angeles Coslado
    • 2
  1. 1.Departamento de FísicaUniversidad de AlcaláAlcalá de Henares, MadridSpain
  2. 2.Departamento de Gestión de la Información Científica IntegradaFundación Española para la Ciencia y la TecnologíaMadridSpain

Personalised recommendations