How does Spearman rho measure a monotonic relationship between ranked variables?

The Spearman rank-order correlation coefficient (Spearman rho) is a nonparametric method designed to quantify the strength of a monotonic relationship between two variables measured on an ordinal or ranked scale.12

A monotonic relationship is one that moves in a constant direction—as one variable increases, the other either consistently increases or consistently decreases, though not necessarily at a constant rate of change. Unlike Pearson’s correlation coefficient, which specifically measures the strength of a linear association between continuous variables, Spearman rho evaluates the association based on the rank orders of the data.23

When using this measure:
* A coefficient of +1 indicates complete agreement in the rankings (a perfect monotonic increase).
* A coefficient of −1 indicates complete disagreement (a perfect monotonic decrease).
* A coefficient of 0 indicates that the rankings are unrelated.1

This approach is particularly useful for data that are not truly interval in nature, such as Likert-scale responses, or when researchers choose to transform interval data into ranks to assess the consistency of a trend.2