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Averages of ratios compared to ratios of averages: Mathematical results

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  • Egghe, L.

Abstract

The recently awakened discussion on the usability of averages of ratios (AoR) compared to ratios of averages (RoA) has led to the mathematical results in this paper. Based on the empirical results in Larivière and Gingras (2011) we prove, under reasonable conditions, the following relations between AoR and RoA for a set of points:(i)The regression line of RoA in function of AoR is the first bisectrix.(ii)(AoR−RoA)/AoR in function of the number N of papers is a cloud of points comprised between a multiple of 1/N and −1/N.(iii)(AoR−RoA)/AoR versus RoA has a decreasing regression line.

Suggested Citation

  • Egghe, L., 2012. "Averages of ratios compared to ratios of averages: Mathematical results," Journal of Informetrics, Elsevier, vol. 6(2), pages 307-317.
    • Handle: RePEc:eee:infome:v:6:y:2012:i:2:p:307-317
    DOI: 10.1016/j.joi.2011.12.007
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    References listed on IDEAS

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    1. Waltman, Ludo & van Eck, Nees Jan & van Leeuwen, Thed N. & Visser, Martijn S. & van Raan, Anthony F.J., 2011. "Towards a new crown indicator: Some theoretical considerations," Journal of Informetrics, Elsevier, vol. 5(1), pages 37-47.
    2. Opthof, Tobias & Leydesdorff, Loet, 2010. "Caveats for the journal and field normalizations in the CWTS (“Leiden”) evaluations of research performance," Journal of Informetrics, Elsevier, vol. 4(3), pages 423-430.
    3. Ludo Waltman & Nees Jan Eck & Thed N. Leeuwen & Martijn S. Visser & Anthony F. J. Raan, 2011. "Towards a new crown indicator: an empirical analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(3), pages 467-481, June.
    4. Larivière, Vincent & Gingras, Yves, 2011. "Averages of ratios vs. ratios of averages: An empirical analysis of four levels of aggregation," Journal of Informetrics, Elsevier, vol. 5(3), pages 392-399.
    5. Leo Egghe & Ronald Rousseau & Guido Van Hooydonk, 2000. "Methods for accrediting publications to authors or countries: Consequences for evaluation studies," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 51(2), pages 145-157.
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    Cited by:

    1. van Zyl, J.M., 2013. "A simulation study to investigate the accuracy of approximating averages of ratios using ratios of averages," Journal of Informetrics, Elsevier, vol. 7(4), pages 907-913.
    2. Loet Leydesdorff, 2013. "An evaluation of impacts in “Nanoscience & nanotechnology”: steps towards standards for citation analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 94(1), pages 35-55, January.
    3. Elio Atenógenes Villaseñor & Ricardo Arencibia-Jorge & Humberto Carrillo-Calvet, 2017. "Multiparametric characterization of scientometric performance profiles assisted by neural networks: a study of Mexican higher education institutions," Scientometrics, Springer;Akadémiai Kiadó, vol. 110(1), pages 77-104, January.
    4. Haruhiko Ogasawara, 2021. "Maximization of Some Types of Information for Unidentified Item Response Models with Guessing Parameters," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 544-563, June.

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