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.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations.
The formula for can be expressed in terms of mean and expectation. Since
the formula for can also be written as
An explicit expression for Kendall's rank coefficient is
Spearman's Rank Correlation Coefficient
- More on Understanding Rho: https://online.stat.psu.edu/stat414/node/113/
- Allen B. Downey, Think Stats: Probability and Statistics for Programmers
- Does Spearmans rho have any advantege over Kendall's tau? https://www.researchgate.net/post/Does_Spearmans_rho_have_any_advantage_over_Kendalls_tau