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

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Abstract

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.

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References

  • Benford, F. (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, 78, 551–572.

    Google Scholar 

  • Cohen, D. (1976). An explanation of first digit phenomenon. Journal of Combinatorial Theory Series A, 20, 367–370.

    Article  MATH  MathSciNet  Google Scholar 

  • Gauvrit, N., & Delahaye, J. P. (2008). A new general explanation of Bendford’s law. Mathematics and Social Sciences, 182, 7–15.

    MATH  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Jolion, J. M. (2001). Images and Benford’s Law. Journal of Mathematical Imaging and Vision, 14, 73–81.

    Article  MATH  MathSciNet  Google Scholar 

  • Judge, G., & Schechter, L. (2009). Detecting problems in survey data using Benford’s law. Journal of Human Resources, 44, 1–24.

    Google Scholar 

  • Kumar, K., & Bhattacharya, S. (2002). Benford’s law and its application in financial fraud detection. Advances in Financial Planning and Forecasting, 11, 57–70.

    Article  Google Scholar 

  • Newcomb, S. (1881). Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics, 4, 39–40.

    Article  MathSciNet  Google Scholar 

  • Ni, D. D., Wei, L., & REN, Z. Z. (2009). Benford’s Law and β-decay half-lives. Communications in Theoretical Physics, 51, 713–716.

    Article  Google Scholar 

  • Pain, J. C. (2008). Benford’s law and complex atomic spectra. Physical Review E, 77, 012008–012102.

    Article  Google Scholar 

  • Shao, L., & Ma, B. Q. (2009). First digit distribution of hadron full width. Modern Physics Letters A, 24, 3275–3282.

    Article  Google Scholar 

Download references

Acknowledgments

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.

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Correspondence to Juan Miguel Campanario.

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Campanario, J.M., Coslado, M.A. Benford’s law and citations, articles and impact factors of scientific journals. Scientometrics 88, 421–432 (2011). https://doi.org/10.1007/s11192-011-0387-9

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