Reminder of some Statistical Values

or

or

For a dataset of n samples, the n values X_i, Y_i are converted to ranks R(X_i), R(Y_i), and the rank correlation is computed as:

On the opposite to the commonly used Pearson correlation, which measures the linear correlation of a bivariate dataset, the Spearman correlation coefficient measures how well the rank of the samples regarding two variables are correlated. It assesses how well the relationship between two variables can be described using a monotonic function (always increase or decrease). For this reason, it is also known as the “rank correlation coefficient”. It is generally used to compare multivariate datasets with complex relationships, such as the input and output dataset of a PPMT workflow. It is less sensitive to outliers than classical correlation since only the rank of the sample is used, and not the measure value itself.

In the following equations, n designates the number of pairs of data separated by the considered distance, Z_i and Z_i+h stands for the value of the variable at two data points i and i+h constituting a pair.