IDEAS home Printed from https://ideas.repec.org/a/jns/jbstat/v233y2013i2p206-224.html
   My bibliography  Save this article

A Coefficient of Correlation Based on Ratios of Ranks and Anti-ranks

Author

Listed:
  • Tarsitano Agostino

    (Dipartimento di Economia e Statistica – Università della Calabria, Via Pietro Bucci, cubo 1C, 87036 Rende (CS), Italy)

  • Lombardo Rosetta

    (Dipartimento di Economia e Statistica – Università della Calabria, Via Pietro Bucci, cubo 0C, 87036 Rende (CS), Italy)

Abstract

Rank association is a fundamental tool to express dependence for ordinal data. Measures of rank correlation have been developed in several contexts for more than a century and we were able to cite more than thirty of these coefficients, from simple ones to relatively complicated definitions involving one or more systems of weights. However, only a few of these can actually be considered reasonable measures of concordance/discordance. The main drawback with the vast majority of coefficients is their resistance-to-change which appears to be of limited value for the purposes of rank comparisons that are intrinsically robust. In this article, a new non-parametric correlation coefficient is defined that is based on ratios of two ranks. In comparing it with existing coefficients, it was found to be extremely sensitive to permutation patterns.We have illustrated the potential improvement that our index may provide in economic contexts by comparing published results with those obtained through the use of this new index. The success that we have had suggests that our index may have important applications wherever the discriminatory power of the rank correlation coefficient ought to be particularly strong.

Suggested Citation

  • Tarsitano Agostino & Lombardo Rosetta, 2013. "A Coefficient of Correlation Based on Ratios of Ranks and Anti-ranks," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(2), pages 206-224, April.
    • Handle: RePEc:jns:jbstat:v:233:y:2013:i:2:p:206-224
    DOI: 10.1515/jbnst-2013-0205
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jbnst-2013-0205
    Download Restriction: no
    File URL: https://libkey.io/10.1515/jbnst-2013-0205?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Neumark, David & Postlewaite, Andrew, 1998. "Relative income concerns and the rise in married women's employment," Journal of Public Economics, Elsevier, vol. 70(1), pages 157-183, October.
    2. William Horrace & Joseph Marchand & Timothy Smeeding, 2008. "Ranking inequality: Applications of multivariate subset selection," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 5-32, March.
    3. Croux, C. & Dehon, C., 2010. "Influence Functions of the Spearman and Kendall Correlation Measures," Other publications TiSEM 5e8ee766-ee1e-4d6e-b035-6, Tilburg University, School of Economics and Management.
    4. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
    5. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    6. Roll, Richard, 1978. "Ambiguity when Performance is Measured by the Securities Market Line," Journal of Finance, American Finance Association, vol. 33(4), pages 1051-1069, September.
    7. Michael Gapen & Dale Gray & Cheng Hoon Lim & Yingbin Xiao, 2008. "Measuring and Analyzing Sovereign Risk with Contingent Claims," IMF Staff Papers, Palgrave Macmillan, vol. 55(1), pages 109-148, April.
    8. Rajarshi Majumder, 2013. "Intergenerational Mobility," SpringerBriefs in Economics, Springer, edition 127, number 978-81-322-1130-3, September.
    9. Majumder, Rajarshi, 2010. "Intergenerational mobility in educational & occupational attainment: a comparative study of social classes in India," MPRA Paper 40939, University Library of Munich, Germany.
    10. Robert J. Hill, 1999. "Comparing Price Levels across Countries Using Minimum-Spanning Trees," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 135-142, February.
    11. Maurizio Brizzi, 1992. "Misure di variabilità, concentrazione e dissomiglianza come sintesi di rapporti," Quaderni di Dipartimento 2, Department of Statistics, University of Bologna.
    12. Rajarshi Majumder, 2010. "Intergenerational Mobility in Educational and Occupational Attainment," Margin: The Journal of Applied Economic Research, National Council of Applied Economic Research, vol. 4(4), pages 463-494, November.
    13. Vito Peragine, 2004. "Ranking Income Distributions According to Equality of Opportunity," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 2(1), pages 11-30, April.
    14. Korhonen, Pekka & Siljamaki, Aapo, 1998. "Ordinal principal component analysis theory and an application," Computational Statistics & Data Analysis, Elsevier, vol. 26(4), pages 411-424, February.
    15. Phelps Brown, E H, 1972. "The Underdevelopment of Economics," Economic Journal, Royal Economic Society, vol. 82(325), pages 1-10, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Agostino Tarsitano & Rosetta Lombardo, 2011. "An Exhaustive Coefficient Of Rank Correlation," Working Papers 201111, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    2. Sripad Motiram & Ashish Singh, 2012. "How close does the apple fall to the tree? Some evidence on intergenerational occupational mobility from India," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2012-017, Indira Gandhi Institute of Development Research, Mumbai, India.
    3. Nandi, Tushar K., 2013. "Intergenerational Persistence of Industry of Employment in India," MPRA Paper 51281, University Library of Munich, Germany.
    4. Reddy, A. Bheemeshwar & Swaminathan, Madhura, 2014. "Intergenerational Occupational Mobility in Rural India: Evidence from Ten Villages," Review of Agrarian Studies, Foundation for Agrarian Studies, vol. 4(01), July.
    5. Majumder, Rajarshi & Ray, Jhilam, 2016. "Development and Exclusion: Intergenerational Stickiness in India," MPRA Paper 71182, University Library of Munich, Germany.
    6. Azam, Mehtabul, 2013. "Intergenerational Occupational Mobility in India," IZA Discussion Papers 7608, Institute of Labor Economics (IZA).
    7. Nandi, Tushar Kanti & Kar, Saibal, 2015. "Short-term Migration and Intergenerational Persistence of Industry in Rural India," IZA Discussion Papers 9283, Institute of Labor Economics (IZA).
    8. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    9. Barati, Hojjat & Yazici, Anil & Almotahari, Amirmasoud, 2024. "A methodology for ranking of critical links in transportation networks based on criticality score distributions," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    10. Vito Peragine & Laura Serlenga, 2008. "Higher education and equality of opportunity in Italy," Research on Economic Inequality, in: Inequality and Opportunity: Papers from the Second ECINEQ Society Meeting, pages 67-97, Emerald Group Publishing Limited.
    11. Pablo Aragonés‐Beltrán & Mª. Carmen González‐Cruz & Astrid León‐Camargo & Rosario Viñoles‐Cebolla, 2023. "Assessment of regional development needs according to criteria based on the Sustainable Development Goals in the Meta Region (Colombia)," Sustainable Development, John Wiley & Sons, Ltd., vol. 31(2), pages 1101-1121, April.
    12. Huo, Yujia & Golley, Jane, 2022. "Intergenerational education transmission in China: The gender dimension," China Economic Review, Elsevier, vol. 71(C).
    13. Nawazuddin Ahmed & Dinesh K. Nauriyal, 2023. "Occupational and Educational Mobility Among Indian Muslims: Primary Survey-Based Evidence," Millennial Asia, , vol. 14(2), pages 228-259, June.
    14. Anirudh Krishna, 2014. "Examining the Structure of Opportunity and Social Mobility in India: Who Becomes an Engineer?," Development and Change, International Institute of Social Studies, vol. 45(1), pages 1-28, January.
    15. Liang Wu & Lin Guan & Feng Li & Qi Zhao & Yingjun Zhuo & Peng Chen & Yaotang Lv, 2018. "Optimal Dynamic Reactive Power Reserve for Wind Farms Addressing Short-Term Voltage Issues Caused by Wind Turbines Tripping," Energies, MDPI, vol. 11(7), pages 1-15, July.
    16. Umut Asan & Ayberk Soyer, 2022. "A Weighted Bonferroni-OWA Operator Based Cumulative Belief Degree Approach to Personnel Selection Based on Automated Video Interview Assessment Data," Mathematics, MDPI, vol. 10(9), pages 1-33, May.
    17. William Horrace & Joseph Marchand & Timothy Smeeding, 2008. "Ranking inequality: Applications of multivariate subset selection," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 5-32, March.
    18. Michael Pfarrhofer, 2024. "Forecasts with Bayesian vector autoregressions under real time conditions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(3), pages 771-801, April.
    19. Muhammad Shehrayar Khan & Atif Rizwan & Muhammad Shahzad Faisal & Tahir Ahmad & Muhammad Saleem Khan & Ghada Atteia, 2022. "Identification of Review Helpfulness Using Novel Textual and Language-Context Features," Mathematics, MDPI, vol. 10(18), pages 1-20, September.
    20. Alvarez, Agustín & Boente, Graciela & Kudraszow, Nadia, 2019. "Robust sieve estimators for functional canonical correlation analysis," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 46-62.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jns:jbstat:v:233:y:2013:i:2:p:206-224. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.