A Comparison of the Pearson, Spearman Rank and Kendall Tau Correlation Coefficients Using Quantitative Variables

Essam F. El-Hashash *

Department of Agronomy, Faculty of Agriculture, Al-Azhar University, Cairo, Egypt.

Raga Hassan Ali Shiekh

Department of Mathematics, College of Mathematical and Statistics Technology, Al-Neelain University, Khartoum, Sudan.

*Author to whom correspondence should be addressed.


Abstract

In all fields and branches of sciences especially statistics, the correlation coefficient is one of the most often used statistical measures. This study has been carried out for comparing the performances of the Pearson (), Spearman's Rank (), and Kendall’s Tau () correlation coefficients under three sample sizes based on the data of quantitative variables of cotton. Descriptive statistics showed the presence of genetic variability for the cotton studied traits in this study. The quantity, significance, and direction of the correlation calculated by  differed in some cases from the other methods under the three sample sizes, opposite is true for  and . The highest number of positive correlations among studied traits were by  under N = 30 observations, and by   and  under N = 20 observations. The studied correlation methods performances by Root Mean Square Error (RMSE) revealed that  and  appear to be a good estimator of correlation because they have the lowest values of RMSE. The highest values of RMSE were observed by  and   under N=10 and N=20, and by   under N=30. The results of PCA could be useful and appropriate in this study, in which the PCA1 had highly positively correlated with the three studied methods for N=10 observations, and with  and  for N=20 observations.

Keywords: Correlation, pearson, Spearman's Rank, Kendall’s Tau, RMSE, PCA


How to Cite

El-Hashash, E. F., & Shiekh, R. H. A. (2022). A Comparison of the Pearson, Spearman Rank and Kendall Tau Correlation Coefficients Using Quantitative Variables. Asian Journal of Probability and Statistics, 20(3), 36–48. https://doi.org/10.9734/ajpas/2022/v20i3425

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References

Sobri NBM, Midi H, Ibrahim NB, Ismail NA, Yaacob WFW, Malik MAA. Differences between pearson’s product moment correlation coefficient and an absolute value correlation coefficient in the presence of outliers. Journal of Mathematics and Computing Science 2016;1(1):1–11.

Etaga HO, Okoro I, Aforka KF, Ngonadi LO. Methods of Estimating Correlation Coefficients in the Presence of Influential Outlier(s). African Journal of Mathematics and Statistics Studies. 2021;4(3):157–185.

DOI: 10.52589/AJMSS-LLNZXUOZ.

Coblick W. Studies in the History of Statistics Method, London: Arno Press; 1998.

Temizhan E, Mirtagioglub H, Mendesc M. Which Correlation Coefficient Should Be Used for Investigating Relations between Quantitative Variables? American Scientific Research Journal for Engineering, Technology, and Sciences. 2022;85(1):265–277.

Wilcox RR. Introduction to Robust Estimation and Hypothesis Testing, 3rd Edn Oxford: Academic Press; 2012.

Tuğran E, Kocak M, Mirtagioğlu H, Yiğit S, Mendes M. A Simulation Based Comparison of Correlation Coefficients with Regard to Type I Error Rate and Power. Journal of Data Analysis and Information Processing. 2015;3:87–101.

DOI: 10.4236/jdaip.2015.33010

Schober P, Boer C, Schwarte LA. Correlation Coefficients: Appropriate Use and Interpretation. Anesthesia & Analgesia. 2018;126(5):1763-–1768.

DOI: 10.1213/ANE.0000000000002864

McCallister C. Phi. Rho. P.M.. Biserial and Point-Biserial “r”: A review of linkages. Paper presented at the annual meeting of the Southwest Educational Research Association, San Antonio, TX; 1991.

El-Hashash EF. Comparison of Variance Components Methods for One Way Random Effects Model in Cotton. Asian Journal of Advances in Agricultural Research. 2017;3(1):1–9.

Available:https://doi.org/10.9734/AJAAR/2017/36955

Carroll JB. The nature of the data, or how to choose a correlation coefficient. Psychometrika. 1961;26:347–372.

Chung YM, Lee JY. A corpus-based approach to comparative evaluation of statistical term association measures. Journal of the American Society for Information Science and Technology. 2001;52:283–96.

Pearson K. Notes on the history of correlation. Biometrika 1920;13(1):25–45.

Spearman C. The proof and measurement of association between two things, 15,72-101. The American Journal of Psychology, 100(3/4), special centennial issue (Autumn Winter,1987),1904;441–471.

DOI: 10.2307/1422689.

de Winter JCF, Gosling SD, Potter J. Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: A tutorial using simulations and empirical data. Psychological Methods. 2016;1(3):273–290.

Available:https://doi.org/10.1037/met0000079

Kendall MG. A new measure of rank correlation. Biometrika, 1938;30:81-93.

Kendall, MG, Gibbons JD. Rank Correlation Methods. Fifth edn. London: Griffin; 1955.

Kendall MG. Rank and product-moment correlation. Biometrika, 1949;36:177–193.

Available:https://doi.org/10.2307/2332540

Sheskin D. Handbook of Parametric and Nonparametric Statistical Procedure (5th ed.). Boca Raton, FL: CRC Press; 2011.

Fisher RA, Immer FR, Tedin O. The genetical interpretation of statistics of the third degree in the study of quantitative inheritance. Genetics. 1932;17(2):107–124,

Available:https://doi.org/10.1093/genetics/17.2.107

Robson DS. Application of K4 statistics to genetic variance component analysis. Biometrics. 1956;12(4):433–444.

Available:https://doi.org/10.2307/3001682

Nachimuthu VV, Robin S, Sudhakar D, Raveendran M, Rajeswari S, Manonmani S. Evaluation of rice genetic diversity and variability in a population panel by principal component analysis. Indian Journal of Science and Technology. 2014;7(10):1555–1562, 2014.

DOI: 10.17485/ijst/2014/v7i10.14

Ponnaiah G, Tannidi S, Manonmani S, Robin S. Estimates of genetic variability, heritability and genetic advance for blast resistance gene introgressed segregating population in rice. International Journal of Current Microbiology and Applied Science. 2017;5(12):672–677. DOI: 10.20546/ijcmas.2016.512.075

Govintharaj P, Manonmani S, Robin S. Variability and genetic diversity study in an advanced segregating population of rice with bacterial blight resistance genes introgressed. Ciência e Agrotecnologia. 2018;42(3):291–296.

Available:https://doi.org/10.1590/1413 70542018423022317

Gomes FP. Curso de estatística experimental. 15.ed. Piracicaba: Esalq. 2009;477.

Yehia WMB, El-Hashash EF. Correlation and multivariate analysis across non-segregation and segregation generations in two cotton crosses. Egyptian Journal of Agricultural Research. 2021;99:354–364.

DOI: 10.21608/EJAR.2021.81571.1117.

El-Hashash EF. Yehia WMB. Estimation of heritability, genes number and multivariate analysis using non- segregation and segregation generations in two cotton crosses. Asian J. of Biochemistry, Genetics and Molecular Biology. 2021;9(3):45–62.

Available:https://doi.org/10.9734/ajbgmb/2021/v9i330221

Hauke J, Kossowski T. Comparison of Values of Pearson's and Spearman's Correlation Coefficients on the Same Sets of Data. Quaestiones Geographicae, 2011;30(2):87–93.

Available:https://doi.org/10.2478/v10117-011-0021-1

Pernet CR, Wilocox RR, Rousselet GA. Robust correlation analyses: false positive and power validation using a new open source Matlab toolbox. Frointiers in Psychology, 2013;3:1–18.

Available:https://doi.org/10.3389/fpsyg.2012.00606

Humphreys RK, Puth MT, Neuhäuser M. Ruxton G. Underestimation of Pearson’s product moment correlation statistic. Oecologia. 2019;189:1–7.

Available:https://doi.org/10.1007/s00442-018-4233-0

Croux C, Dehon C. Influence functions of the Spearman and Kendall correlation measures. Statistical Methods and Applications, 2010;19:497–515.

Available:http://dx.doi.org/10.1007/s10260-010-0142-z

Xu W, Hou Y, Hung YS, Zou Y. A comparative analysis of Spearman’s rho and Kendall’s tau in normal and contaminated normal models. Signal Processing. 2013;93:261–276.

Available:http://dx.doi.org/10.1016/j.sigpro.2012.08.005

Sharma R, Mukherjee A, Jassal HK. Reconstruction of latetime cosmology using principal component analysis. The European Physical Journal Plus, 2022;137: 219.

Available:https://doi.org/10.1140/epjp/s13360-022-02397-0

El-Hashash, E.F. Genetic Diversity of Soybean Yield Based on Cluster and Principal Component Analyses. Journal of Advances in Biology & Biotechnology. 2016; 10:1–9. Available:https://doi.org/10.9734/JABB/2016/29127

El-Hashash EF, Abou El-Enin MM, Abd El-Mageed TA, Attia MAE-H, El-Saadony MT, El-Tarabily KA, Shaaban A. Bread Wheat Productivity in Response to Humic Acid Supply and Supplementary Irrigation Mode in Three Northwestern Coastal Sites of Egypt. Agronomy. 2022;12(7):1499.

Available:https://doi.org/10.3390/agronomy12071499

El Sherbiny HA, El-Hashash EF, Abou El-Enin MM, Nofal RS, Abd El-Mageed TA, Bleih EM, El-Saadony MT, El-Tarabily KA, Shaaban A. Exogenously Applied Salicylic Acid Boosts Morpho-Physiological Traits, Yield, and Water Productivity of Lowland Rice under Normal and Deficit Irrigation. Agronomy. 2022;12(8):1860.

Available:https://doi.org/10.3390/agronomy12081860

Ahad NA, Zakaria NA, Abdullah S, Syed Yahaya SS, Yusof N. Robust Correlation Procedure via Sn Estimator. Journal of Telecommunication, Electronic and Computer Engineering (JTEC). 2018;10(1-10):115–118.

Available:https://jtec.utem.edu.my/jtec/article/view/3801

Li G, Peng H, Zhang J., Zhu L. Robust Rank Correlation Based Screening. The Annals of Statistics. 2012;40(3):1846–1877.

DOI: 10.1214/12-AOS1024.