Journal of Guangdong University of Technology ›› 2012, Vol. 29 ›› Issue (3): 12-17.doi: 10.3969/j.issn.1007-7162.2012.03.002

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A Review on Correlation Coefficients

Xu Wei-chao   

  1. School of Automation, Guangdong University of Technology, Guangzhou 510006, China
  • Received:2012-06-03 Online:2012-09-20 Published:2012-09-20

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Abstract: As statistics characterizing the strength of statistical relationship between two random variables,correlation coefficients have found wide applications in nearly all science and technology  fields.This  paper attempts to provide a detailed review on 5 commonly used correlation coeffcients in the literature, including a relatively detailed discussion on their statistical properties under the fundamental bivariate normal model and their suitable application scenarios. Specifically,(1) if the sample follows normal distribution, then the  Pearsons Product Moment Correlation Coefficient is optimal;(2) if the monotone nonlinear distortion in the sample is small, then the Order Statistics Correlation Coefficient should be used;(3) if the monotone nonlinear distortion in the sample is severe, then the Spearmans rho or Kendalls tau are feasible;(4) if only one channel is distorted by monotone nonlinearity, then the Gini Correlation is best choice; and (5) if there exsits impulsive noise in the sample, then  the Spearmans rho or Kendalls tau should be employed.

Key words: Pearson‘s Product Moment Correlation Coefficient (PPMCC); Spearman’s Rho (SR); Kendall‘s Tau (KT);Order Statistics Correlation Coefficient (OSCC); Gini Correlation (GC); Bivariate No

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