Estimators for correlation and association

Estimators for correlation/association and their properties and assumptions.

Estimator Purpose
Pearson r Estimate the Pearson rho correlation coefficient using the sample Pearson correlation coefficient r.

Use when a linear function best describes the relationship between the variables.

Susceptible to outliers. Assumes a bivariate normal distribution.

Spearman rs Estimate the Spearman rho rank correlation coefficient using the sample Spearman rs correlation coefficient.

Use when a monotonic function best describes the relationship between variables.

Kendall tau Estimate the Kendall tau rank correlation coefficient.

Use when a monotonic function best describes the relationship between the variables. Preferred instead of Spearman correlation because Kendall's tau is the difference between the probability that the two variables are in the same order, versus the probability that the two variables are in different orders.

Robust to outliers.