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Research Article Open access CC BY 4.0

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

Essam F. El-Hashash, Raga Hassan Ali Shiekh

Asian Journal of Probability and Statistics · pp. 36–48 · Published 18 Oct 2022

10.9734/ajpas/2022/v20i3425

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.

Correlation pearson Spearman's Rank Kendall’s Tau RMSE PCA

References (31)

  1. 1 Correlation Coefficients: Appropriate Use and Interpretation [DOI]
  2. 2 A NEW MEASURE OF RANK CORRELATION [DOI]
  3. 3 Introduction to Robust Estimation and Hypothesis Testing [DOI]
  4. 4 Comparison of Values of Pearson's and Spearman's Correlation Coefficients on the Same Sets of Data [DOI]
  5. 5 Rank Correlation Methods. [DOI]
  6. 6 Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: A tutorial using simulations and empirical data. [DOI]
  7. 7 The Proof and Measurement of Association between Two Things [DOI]
  8. 8 NOTES ON THE HISTORY OF CORRELATION [DOI]
  9. 9 Influence functions of the Spearman and Kendall correlation measures [DOI]
  10. 10 Robust Correlation Analyses: False Positive and Power Validation Using a New Open Source Matlab Toolbox [DOI]
  11. 11 The Nature of the Data, or How to Choose a Correlation Coefficient [DOI]
  12. 12 Robust rank correlation based screening [DOI]
  13. 13 THE GENETICAL INTERPRETATION OF STATISTICS OF THE THIRD DEGREE IN THE STUDY OF QUANTITATIVE INHERITANCE [DOI]
  14. 14 A comparative analysis of Spearman's rho and Kendall's tau in normal and contaminated normal models [DOI]
  15. 15 Evaluation of Rice Genetic Diversity and Variability in a Population Panel by Principal Component Analysis [DOI]
  16. 16 Underestimation of Pearson’s product moment correlation statistic [DOI]
  17. 17 RANK AND PRODUCT-MOMENT CORRELATION [DOI]
  18. 18 A corpus-based approach to comparative evaluation of statistical term association measures [DOI]
  19. 19 Applications of the k 4 Statistic to Genetic Variance Component Analyses [DOI]
  20. 20 Bread Wheat Productivity in Response to Humic Acid Supply and Supplementary Irrigation Mode in Three Northwestern Coastal Sites of Egypt [DOI]
  21. 21 Exogenously Applied Salicylic Acid Boosts Morpho-Physiological Traits, Yield, and Water Productivity of Lowland Rice under Normal and Deficit Irrigation [DOI]
  22. 22 A Simulation Based Comparison of Correlation Coefficients with Regard to Type I Error Rate and Power [DOI]
  23. 23 Genetic Diversity of Soybean Yield Based on Cluster and Principal Component Analyses [DOI]
  24. 24 Correlation and multivariate analysis across non-segregation and segregation generations in two cotton crosses [DOI]
  25. 25 Reconstruction of latetime cosmology using principal component analysis [DOI]
  26. 26 Estimates of Genetic Variability, Heritability and Genetic Advance for Blast Resistance Gene Introgressed Segregating Population in Rice [DOI]
  27. 27 Estimation of Heritability, Genes Number and Multivariate Analysis Using Non- segregation and Segregation Generations in Two Cotton Crosses [DOI]
  28. 28 Differences Between Pearson’s Product Moment Correlation Coefficient and An Absolute Value Correlation Coefficient in the Presence of Outliers
  29. 29 Robust Correlation Procedure via Sn Estimator
  30. 30 Methods of Estimating Correlation Coefficients in the Presence of Influential Outlier(s) [DOI]
  31. 31 Comparison of Variance Components Methods for One Way Random Effects Model in Cotton [DOI]

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