As mentioned above, when the underlying data is not normal or when the presence of outliers distorts the picture the Spearman’s rank correlation is a non-parametric test that can be used instead of the Pearson’s correlation coefficient.
Definition 1: The Spearman’s rank correlation (also called Spearman’s rho) is the correlation coefficient on the ranks of the data.
Observation: For low values of rho, a table of critical values can be used (see Spearman’s Rho Table). For higher values, Theorem 1 of One Sample Hypothesis Testing for Correlation is applied using Spearman’s rho in place of r, although there isn’t general agreement about the validity of this approach. For this reason, Kendall’s tau is often the preferred non-parametric approach.
For additional information and some examples click here.