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The precision of the arithmetic mean, geometric mean and percentiles for citation data: An experimental simulation modelling approach

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  • Thelwall, Mike

Abstract

When comparing the citation impact of nations, departments or other groups of researchers within individual fields, three approaches have been proposed: arithmetic means, geometric means, and percentage in the top X%. This article compares the precision of these statistics using 97 trillion experimentally simulated citation counts from 6875 sets of different parameters (although all having the same scale parameter) based upon the discretised lognormal distribution with limits from 1000 repetitions for each parameter set. The results show that the geometric mean is the most precise, closely followed by the percentage of a country's articles in the top 50% most cited articles for a field, year and document type. Thus the geometric mean citation count is recommended for future citation-based comparisons between nations. The percentage of a country's articles in the top 1% most cited is a particularly imprecise indicator and is not recommended for international comparisons based on individual fields. Moreover, whereas standard confidence interval formulae for the geometric mean appear to be accurate, confidence interval formulae are less accurate and consistent for percentile indicators. These recommendations assume that the scale parameters of the samples are the same but the choice of indicator is complex and partly conceptual if they are not.

Suggested Citation

  • Thelwall, Mike, 2016. "The precision of the arithmetic mean, geometric mean and percentiles for citation data: An experimental simulation modelling approach," Journal of Informetrics, Elsevier, vol. 10(1), pages 110-123.
  • Handle: RePEc:eee:infome:v:10:y:2016:i:1:p:110-123
    DOI: 10.1016/j.joi.2015.12.001
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    References listed on IDEAS

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    1. Thelwall, Mike & Wilson, Paul, 2014. "Regression for citation data: An evaluation of different methods," Journal of Informetrics, Elsevier, vol. 8(4), pages 963-971.
    2. Schneider, Jesper W., 2013. "Caveats for using statistical significance tests in research assessments," Journal of Informetrics, Elsevier, vol. 7(1), pages 50-62.
    3. Fairclough, Ruth & Thelwall, Mike, 2015. "More precise methods for national research citation impact comparisons," Journal of Informetrics, Elsevier, vol. 9(4), pages 895-906.
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    6. Fairclough, Ruth & Thelwall, Mike, 2015. "National research impact indicators from Mendeley readers," Journal of Informetrics, Elsevier, vol. 9(4), pages 845-859.
    7. Ludo Waltman & Michael Schreiber, 2013. "On the calculation of percentile-based bibliometric indicators," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 64(2), pages 372-379, February.
    8. Bornmann, Lutz & Leydesdorff, Loet & Mutz, Rüdiger, 2013. "The use of percentiles and percentile rank classes in the analysis of bibliometric data: Opportunities and limits," Journal of Informetrics, Elsevier, vol. 7(1), pages 158-165.
    9. Aksnes, Dag W. & Schneider, Jesper W. & Gunnarsson, Magnus, 2012. "Ranking national research systems by citation indicators. A comparative analysis using whole and fractionalised counting methods," Journal of Informetrics, Elsevier, vol. 6(1), pages 36-43.
    10. Abramo, Giovanni & D’Angelo, Ciriaco Andrea, 2015. "The relationship between the number of authors of a publication, its citations and the impact factor of the publishing journal: Evidence from Italy," Journal of Informetrics, Elsevier, vol. 9(4), pages 746-761.
    11. Giovanni Abramo & Ciriaco Andrea D'Angelo, 2015. "The VQR, Italy's second national research assessment: Methodological failures and ranking distortions," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 66(11), pages 2202-2214, November.
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    14. Thelwall, Mike & Sud, Pardeep, 2016. "National, disciplinary and temporal variations in the extent to which articles with more authors have more impact: Evidence from a geometric field normalised citation indicator," Journal of Informetrics, Elsevier, vol. 10(1), pages 48-61.
    15. Asmussen, Søren & Rojas-Nandayapa, Leonardo, 2008. "Asymptotics of sums of lognormal random variables with Gaussian copula," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2709-2714, November.
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    Citations

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    Cited by:

    1. Thelwall, Mike, 2017. "Three practical field normalised alternative indicator formulae for research evaluation," Journal of Informetrics, Elsevier, vol. 11(1), pages 128-151.
    2. Rodríguez-Navarro, Alonso & Brito, Ricardo, 2018. "Double rank analysis for research assessment," Journal of Informetrics, Elsevier, vol. 12(1), pages 31-41.
    3. Vîiu, Gabriel-Alexandru, 2018. "The lognormal distribution explains the remarkable pattern documented by characteristic scores and scales in scientometrics," Journal of Informetrics, Elsevier, vol. 12(2), pages 401-415.
    4. Mike Thelwall, 2018. "Differences between journals and years in the proportions of students, researchers and faculty registering Mendeley articles," Scientometrics, Springer;Akadémiai Kiadó, vol. 115(2), pages 717-729, May.
    5. Fei Shu & Wen Lou & Stefanie Haustein, 2018. "Can Twitter increase the visibility of Chinese publications?," Scientometrics, Springer;Akadémiai Kiadó, vol. 116(1), pages 505-519, July.
    6. Thelwall, Mike, 2016. "Are there too many uncited articles? Zero inflated variants of the discretised lognormal and hooked power law distributions," Journal of Informetrics, Elsevier, vol. 10(2), pages 622-633.
    7. Thelwall, Mike, 2016. "Are the discretised lognormal and hooked power law distributions plausible for citation data?," Journal of Informetrics, Elsevier, vol. 10(2), pages 454-470.
    8. Waltman, Ludo, 2016. "A review of the literature on citation impact indicators," Journal of Informetrics, Elsevier, vol. 10(2), pages 365-391.
    9. Thelwall, Mike, 2016. "The discretised lognormal and hooked power law distributions for complete citation data: Best options for modelling and regression," Journal of Informetrics, Elsevier, vol. 10(2), pages 336-346.
    10. Thelwall, Mike, 2018. "Do females create higher impact research? Scopus citations and Mendeley readers for articles from five countries," Journal of Informetrics, Elsevier, vol. 12(4), pages 1031-1041.
    11. Kousha, Kayvan & Thelwall, Mike, 2018. "Can Microsoft Academic help to assess the citation impact of academic books?," Journal of Informetrics, Elsevier, vol. 12(3), pages 972-984.

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