[Statistics] Comparison of Three Correlation Coefficients: Pearson, Kendall, Spearman

There are three popular metrics to measure the correlation between two random variables: Pearson's correlation coefficient, Kendall's tau and Spearman's rank correlation coefficient. In this article, I will make a detailed comparison among the three measures and discuss how to choose among them.

Definition

Pearson Correlation

 Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. 

 The formula for \rho  can be expressed in terms of mean and expectation. Since

the formula for \rho  can also be written as

Kendall's Tau

An explicit expression for Kendall's rank coefficient is 

{\displaystyle \tau ={\frac {2}{n(n-1)}}\sum _{i<j}\operatorname {sgn}(x_{i}-x_{j})\operatorname {sgn}(y_{i}-y_{j})}. 

Spearman's Rank Correlation Coefficient

 

Comparison

 

 

Reference

 

posted @ 2020-03-04 03:34  Sherrrry  阅读(302)  评论(0)  编辑  收藏  举报