Spearman rank correlation evaluates the strength and direction of a monotonic relationship between two variables.
A relationship is monotonic if one variable never decreases as the other increases, or never increases as the other increases.
Unlike Pearson correlation, Spearman rank correlation does not require the relationship to follow a straight line.
It operates by converting raw numerical observations into ordinal ranks from lowest to highest for each variable.
The lowest observation receives rank one, the second lowest receives rank two, and tied values receive averaged ranks.
Once ranks are assigned, the Pearson correlation coefficient is computed directly on the ranked numbers.
The resulting Spearman coefficient, denoted as rho, ranges from negative one to positive one.
A value of positive one indicates a perfect monotonic relationship where higher values in X always accompany higher values in Y.
For example, an exponential relationship where Y equals two to the power of X yields a perfect Spearman correlation of one.
Pearson correlation on the same exponential curve yields a value below one because the curve bends away from a line.
Because it calculates on ranks rather than raw magnitudes, Spearman correlation is robust against extreme outliers.
An outlier located far along the axis is constrained to the next available rank integer, limiting its mathematical leverage.
Spearman correlation is also ideal for analysing ordinal survey responses, such as customer satisfaction ratings.
However, converting continuous data to ranks discards precise distance information between neighbouring observations.
Analysts use Spearman correlation whenever features exhibit non-linear monotonic trends or contain heavy-tailed outliers.