Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Quaestiones Geographicae

The Journal of Adam Mickiewicz University

4 Issues per year


CiteScore 2016: 0.43

SCImago Journal Rank (SJR) 2016: 0.258
Source Normalized Impact per Paper (SNIP) 2016: 0.359

Open Access
Online
ISSN
2081-6383
See all formats and pricing
More options …

Comparison of Values of Pearson's and Spearman's Correlation Coefficients on the Same Sets of Data

Jan Hauke
  • Institute of Socio-Economic Geography and Spatial Management, Adam Mickiewicz University, Poznań, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Tomasz Kossowski
  • Institute of Socio-Economic Geography and Spatial Management, Adam Mickiewicz University, Poznań, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2011-06-24 | DOI: https://doi.org/10.2478/v10117-011-0021-1

Comparison of Values of Pearson's and Spearman's Correlation Coefficients on the Same Sets of Data

Spearman's rank correlation coefficient is a nonparametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of an association between two variables. It is a measure of a monotone association that is used when the distribution of data makes Pearson's correlation coefficient undesirable or misleading. Spearman's coefficient is not a measure of the linear relationship between two variables, as some "statisticians" declare. It assesses how well an arbitrary monotonic function can describe a relationship between two variables, without making any assumptions about the frequency distribution of the variables. Unlike Pearson's product-moment correlation coefficient, it does not require the assumption that the relationship between the variables is linear, nor does it require the variables to be measured on interval scales; it can be used for variables measured at the ordinal level. The idea of the paper is to compare the values of Pearson's product-moment correlation coefficient and Spearman's rank correlation coefficient as well as their statistical significance for different sets of data (original - for Pearson's coefficient, and ranked data for Spearman's coefficient) describing regional indices of socio-economic development.

Keywords: Pearson's correlation coefficient; Spearman's rank correlation coefficient; Kendall's tau; regional indices of socio-economic development

  • Anderson T.W., 1996. R.A. Fisher and multivariate analysis. Statistical Science 11 (1): 20-34.Google Scholar

  • Bravais A., 1846. Analyse mathématique sur les probabilités des erreurs de situation d'un point. Mémoires présentés par divers savants à l'Académie Royale des Sciences de l'Institut de France 9: 255-332.Google Scholar

  • Daniels H.E., 1944. The relation between measures of correlation in the universe of sample permutations. Biometrika 33 (2): 129-135.CrossrefGoogle Scholar

  • Fisher R.A., 1915. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 10: 507-521.Google Scholar

  • Fisher R.A., 1921. On the "probable error" of a coefficient of correlation deduced from a small sample. Metron 1: 3-32.Google Scholar

  • Galton F., 1869. Hereditary genius. An inquiry into its laws and consequences. MacMillan, London.Google Scholar

  • Galton F., 1875. Statistics by intercomparison. Philosophical Magazine 49: 33-46.Google Scholar

  • Galton F., 1885. Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute 15: 246-263.Google Scholar

  • Galton F., 1877. Typical laws of heredity. Proceedings of the Royal Institution 8: 282-301.Google Scholar

  • Galton F., 1888. Co-relations and their measurement, chiefly from anthropometric data. Proceedings of the Royal Society of London 45: 135-145.CrossrefGoogle Scholar

  • Galton F., 1890. Kinship and correlation. North American Review 150: 419-431.Google Scholar

  • Griffith D.A., 2003. Spatial autocorrelation and spatial filtering. Springer, Berlin.Google Scholar

  • Haining R., 1991. Bivariate correlation with spatial data. Geographical Analysis 23 (3): 210-227.Google Scholar

  • Kendall M.G., 1938. A new measure of rank correlation. Biometrika 30: 81-89.Google Scholar

  • Kendall M.G., 1948. Rank correlation methods. 4th ed. Griffin, London.Google Scholar

  • Pearson K., 1896. Mathematical contributions to the theory of evolution. III. Regression, heredity, and panmixia. Philosophical Transactions of the Royal Society Ser. A 187: 253-318.Google Scholar

  • Pearson K., 1900. Mathematical contributions to the theory of evolution. VII. On the correlation of characters not quantitatively measurable. Philosophical Transactions of the Royal Society Ser. A 195: 1-47.Google Scholar

  • Pearson K., 1920. Notes on the history of correlation. Biometrika 13: 25-45.CrossrefGoogle Scholar

  • Piovani J.I., 2008. The historical construction of correlation as a conceptual and operative instrument for empirical research. Quality & Quantity 42: 757-777.Web of ScienceGoogle Scholar

  • Plata S., 2006. A note on Fisher's correlation coefficient. Applied Mathematical Letters 19: 499-502.Google Scholar

  • Rodgers J.L. & Nicewander W.A., 1988. Thirteen ways to look at the correlation coefficient. The American Statistician 42 (1): 59-66.CrossrefGoogle Scholar

  • Spearman C.E, 1904a. The proof and measurement of association between two things. American Journal of Psychology 15: 72-101.CrossrefGoogle Scholar

  • Spearman C.E, 1904b. General intelligence, objectively determined and measured. American Journal of Psychology 15: 201-293.CrossrefGoogle Scholar

  • Spearman C.E., 1910. Correlation calculated from faulty data. British Journal of Psychology 3: 271-295.Google Scholar

  • Stigler S.M., 1988. Francis Galton's account of the invention of correlation. Statistical Science 4 (2): 73-86.Google Scholar

  • Student, 1908. Probable error of a correlation coefficient. Biometrika 6: 302-310.Google Scholar

  • Valz P.D. & Thompson M.E., 1994. Exact inference for Kendall's S and Spearman's rho. Journal of Computational and Graphical Statistics 3: 459-472.CrossrefGoogle Scholar

  • Walker H. M., 1928. The relation of Plana and Bravais to theory of correlation. Isis 10 (2): 466-484.CrossrefGoogle Scholar

  • Weida F.M., 1927. On various conceptions of correlation. The Annals of Mathematics, Second Series 29 (1/4): 276-312.CrossrefGoogle Scholar

  • Xu Weichao, Yunhe Hou, Hung Y. S. & Yuexian Zou, 2010. Comparison of Spearman's rho and Kendall's tau in normal and contaminated normal models. Manuscript submitted to IEEE Transactions on Information Theory ( http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.2009v1.pdf

  • Yule G.U., 1897a. On the significance of Bravais' formulae for regression, in the case of skew correlation. Proceedings of the Royal Society of London Ser. A 60: 477-489.Google Scholar

  • Yule G.U., 1897b. On the theory of correlation. Journal of the Royal Statistical Society Ser. A 60: 812-854.Google Scholar

  • Yule G.U., 1903. Notes on the theory of association of attributes in statistics. Biometrika 2: 121-134.CrossrefGoogle Scholar

  • Yule G.U., 1907. On the theory of correlation for any number of variables, treated by a new system of notation. Proceedings of the Royal Society of London 79: 182-193.CrossrefGoogle Scholar

About the article


Published Online: 2011-06-24

Published in Print: 2011-06-01


Citation Information: Quaestiones Geographicae, Volume 30, Issue 2, Pages 87–93, ISSN (Print) 0137-477X, DOI: https://doi.org/10.2478/v10117-011-0021-1.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Prajal Pradhan, Luís Costa, Diego Rybski, Wolfgang Lucht, and Jürgen P. Kropp
Earth's Future, 2017
[2]
Fekadu Gurmu, Hussein A Shimelis, and Mark D Laing
South African Journal of Plant and Soil, 2017, Page 1
[3]
Renan S. Lima, Guilherme C. Danielski, and Ana Clarissa S. Pires
Food and Bioprocess Technology, 2017
[5]
Feng Xu, Yan Shi, Min Deng, Jian-ya Gong, Qi-liang Liu, and Rui Jin
Journal of Central South University, 2017, Volume 24, Number 10, Page 2438
[7]
Maitiniyazi Maimaitijiang, Abduwasit Ghulam, Paheding Sidike, Sean Hartling, Matthew Maimaitiyiming, Kyle Peterson, Ethan Shavers, Jack Fishman, Jim Peterson, Suhas Kadam, Joel Burken, and Felix Fritschi
ISPRS Journal of Photogrammetry and Remote Sensing, 2017, Volume 134, Page 43
[8]
Muhammad Farooq, Hikmat Ullah Khan, Saqib Iqbal, Ehsan Ullah Munir, and Ajmal Shahzad
IEEE Access, 2017, Volume 5, Page 19588
[9]
Vito Modesto Manghisi, Michele Gattullo, Michele Fiorentino, Antonio Emmanuele Uva, Francescomaria Marino, Vitoantonio Bevilacqua, and Giuseppe Monno
Presence: Teleoperators and Virtual Environments, 2017, Volume 26, Number 1, Page 1
[10]
Th. I. Götz, G. Lahmer, V. Strnad, Ch. Bert, B. Hensel, A. M. Tomé, E. W. Lang, and Richard Mankin
PLOS ONE, 2017, Volume 12, Number 9, Page e0183608
[12]
Justin Murfitt and Laura C. Brown
Hydrological Processes, 2017
[13]
Thiago Bruno Caparelli and Eduardo Lázaro Martins Naves
Research on Biomedical Engineering, 2017, Number 0
[14]
Shiau Wei Chan, Md Fauzi Ahmad, and Mei Wan Kong
IOP Conference Series: Materials Science and Engineering, 2017, Volume 226, Page 012025
[16]
Xue Fa Tong, M.Y. Jaaffar, A. Abdullah Sani, and A. Muhammad
SHS Web of Conferences, 2017, Volume 36, Page 00012
[17]
Jie Qi, Liang Ma, Xiaogang Wang, Ying Li, and Kejun Wang
Cancer Biomarkers, 2017, Volume 20, Number 1, Page 87
[20]
Meghan Leaver and Tom W. Reader
Human Factors: The Journal of the Human Factors and Ergonomics Society, 2016, Volume 58, Number 6, Page 814
[21]
Andreas Ch. Weber, Veerle De Bosscher, and Hippolyt Kempf
European Sport Management Quarterly, 2017, Page 1
[22]
Rui Pinto, Luís Miguel Brito, and João Coutinho
Biological Agriculture & Horticulture, 2017, Page 1
[23]
Iliana Karina Dominguez-Guerrero, Samantha del Rocío Mariscal-Lucero, José Ciro Hernández-Díaz, Berthold Heinze, José Ángel Prieto-Ruiz, and Christian Wehenkel
PeerJ, 2017, Volume 5, Page e3452
[25]
Muhammad Arslan Usman, Soo Young Shin, Muhammad Shahid, and Benny Lövström
IETE Technical Review, 2017, Volume 34, Number 3, Page 309
[26]
Lilian Anne Krug, Trevor Platt, Shubha Sathyendranath, and Ana B. Barbosa
Remote Sensing of Environment, 2017
[27]
Marcela do Carmo Silva, Luiz Octávio Gavião, Carlos Francisco Simões Gomes, and Gilson Brito Alves Lima
RAI Revista de Administração e Inovação, 2017, Volume 14, Number 3, Page 188
[28]
Man Jiang, Weiwei Sun, Gang Yang, and Dianfa Zhang
Remote Sensing, 2017, Volume 9, Number 4, Page 346
[29]
Guy Sion
Laterality: Asymmetries of Body, Brain and Cognition, 2017, Page 1
[32]
Eoin M. Everard, Andrew J. Harrison, and Mark Lyons
Journal of Strength and Conditioning Research, 2017, Volume 31, Number 5, Page 1265
[33]
Fiorella Acquaotta, Gianluigi Ardissino, Simona Fratianni, and Michela Perrone
International Journal of Biometeorology, 2017
[34]
C. Berger, J. Rosentreter, M. Voltersen, C. Baumgart, C. Schmullius, and S. Hese
Remote Sensing of Environment, 2017, Volume 193, Page 225
[35]
[36]
Jinquan Wang, Jian Cheng, Chao Zhang, and Xiaojun Li
Computational and Mathematical Methods in Medicine, 2017, Volume 2017, Page 1
[37]
Liang Zhu, Christine Lim, Wenjun Xie, and Yuan Wu
Tourism Economics, 2017, Page 135481661769396
[38]
[39]
Michael T. Geier
Journal of Leadership & Organizational Studies, 2016, Volume 23, Number 3, Page 234
[40]
John Gichimu Mbaka, Celia Somlai, Denis Köpfer, Andreas Maeck, Andreas Lorke, Ralf B. Schäfer, and David William Pond
PLoS ONE, 2014, Volume 9, Number 10, Page e111392
[44]
Darío Baptista, Sandy Abreu, Carlos Travieso-González, and Fernando Morgado-Dias
Microprocessors and Microsystems, 2017, Volume 49, Page 77
[45]
James A. Sidney, Ashlin Jones, Carter Coberley, James E. Pope, and Aaron Wells
Health Services and Outcomes Research Methodology, 2017, Volume 17, Number 1, Page 84
[46]
[47]
Emily Dalton, Natasha A. Lannin, Kate Laver, Leo Ross, Stephen Ashford, Annie McCluskey, and Anne Cusick
Disability and Rehabilitation, 2016, Page 1
[48]
Jiling Cao, Youzhi Feng, Xiangui Lin, Junhua Wang, and Xinqiao Xie
Journal of Soils and Sediments, 2017, Volume 17, Number 3, Page 841
[49]
Amir Abolhassani, Ky Layfield, and Bhaskaran Gopalakrishnan
International Journal of Productivity and Performance Management, 2016, Volume 65, Number 7, Page 875
[50]
Jianhua Ni, Tianlu Qian, Changbai Xi, Yikang Rui, and Jiechen Wang
International Journal of Environmental Research and Public Health, 2016, Volume 13, Number 8, Page 833
[51]
Peter McGarry, Sam Clifford, Luke D. Knibbs, Congrong He, and Lidia Morawska
Journal of Occupational and Environmental Hygiene, 2016, Volume 13, Number 10, Page D175
[52]
Yvonne Lichtblau, Karin Zimmermann, Berit Haldemann, Dido Lenze, Michael Hummel, and Ulf Leser
Briefings in Bioinformatics, 2016, Page bbw061
[53]
Chundi Chen, Shengjun Wu, Colin Douglas Meurk, Maohua Ma, Juanjuan Zhao, mingquan Lv, and Xiaoxiao Tong
Landscape and Urban Planning, 2017, Volume 157, Page 45
[54]
[55]
Raymond Aabeyir, Stephen Adu-Bredu, Wilson Agyei Agyare, and Michael J.C. Weir
Energy for Sustainable Development, 2016, Volume 33, Page 84
[56]
Sophie Wiglesworth and Louise Farnworth
Occupational Therapy International, 2016, Volume 23, Number 3, Page 255
[57]
Benjamin Walker, Sepand Alavifard, Surain Roberts, Andrea Lanes, Tim Ramsay, and Sylvain Boet
Health Information & Libraries Journal, 2016, Volume 33, Number 2, Page 140
[58]
Shahana Wadood, Behrooz Gharleghi, and Behrang Samadi
Procedia Economics and Finance, 2016, Volume 37, Page 129
[59]
W. Xu, J. Xu, J. Zhao, and J. Sun
Journal of Instrumentation, 2016, Volume 11, Number 04, Page C04002
[60]
David Provencher, Marie Hennebelle, Stephen C. Cunnane, Yves Bérubé-Lauzière, and Kevin Whittingstall
Frontiers in Aging Neuroscience, 2016, Volume 8
[61]
Nurul Aisyah Sim Abdullah, Nor Laila Mohd Noor, and Emma Nuraihan Mior Ibrahim
Transforming Government: People, Process and Policy, 2016, Volume 10, Number 1, Page 120
[62]
Peng Wu, Rong Bi, Shanshan Duan, Haiyan Jin, Jianfang Chen, Qiang Hao, Yuming Cai, Xinyan Mao, and Meixun Zhao
Journal of Geophysical Research: Biogeosciences, 2016, Volume 121, Number 1, Page 109
[63]
Jia Gao, Wei Wang, and Ji Zhang
Computational Intelligence and Neuroscience, 2016, Volume 2016, Page 1
[64]
Beatriz Rodríguez-Martín, Minna Stolt, Jouko Katajisto, and Riitta Suhonen
Scandinavian Journal of Caring Sciences, 2016, Volume 30, Number 2, Page 250
[65]
Sofie Boterberg and Petra Warreyn
Personality and Individual Differences, 2016, Volume 92, Page 80
[66]
Chengwei Xiao, Jiaqi Ye, Rui Máximo Esteves, and Chunming Rong
Concurrency and Computation: Practice and Experience, 2016, Volume 28, Number 14, Page 3866
[67]
Noor Ezan Abdullah, Hadzli Hashim, Muhammad Fathullah Sulaiman, Nina Korlina Madzhi, Ahmad Faiz Mohd Sampian, and Faridatul Aima Ismail
IOP Conference Series: Materials Science and Engineering, 2015, Volume 99, Page 012014
[68]
Peipei Li, Yongjun Piao, Ho Sun Shon, and Keun Ho Ryu
BMC Bioinformatics, 2015, Volume 16, Number 1
[69]
Elizabeth A. Freeman, Gretchen G. Moisen, John W. Coulston, and Barry T. Wilson
Canadian Journal of Forest Research, 2016, Volume 46, Number 3, Page 323
[70]
Shaurya Jauhari and S. A. M. Rizvi
IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2014, Volume 11, Number 3, Page 533
[71]
Nagesh Kolagani, Palaniappan Ramu, and Koshy Varghese
JAWRA Journal of the American Water Resources Association, 2015, Volume 51, Number 6, Page 1708
[72]
Trevor van Mierlo, Douglas Hyatt, and Andrew T Ching
Journal of Medical Internet Research, 2015, Volume 17, Number 6, Page e160
[73]
J. G. Mbaka and R. B. Schäfer
River Research and Applications, 2016, Volume 32, Number 5, Page 907
[74]
Goran Putnik, Eric Costa, Cátia Alves, Hélio Castro, Leonilde Varela, and Vaibhav Shah
International Journal of Technology and Design Education, 2016, Volume 26, Number 3, Page 413
[75]
Ruibo Sun, Xue-Xian Zhang, Xisheng Guo, Daozhong Wang, and Haiyan Chu
Soil Biology and Biochemistry, 2015, Volume 88, Page 9
[76]
Natalia Cichoń, Michał Bijak, Elżbieta Miller, Marta Niwald, and Joanna Saluk
Oxidative Medicine and Cellular Longevity, 2015, Volume 2015, Page 1
[77]
Judit Bar-Ilan and Mark Levene
Scientometrics, 2015, Volume 102, Number 3, Page 2247
[79]

Comments (0)

Please log in or register to comment.
Log in