Spearmankorrelation

SpearmanKorrelation, commonly called Spearman's rank correlation coefficient, is a nonparametric measure of statistical dependence between two variables. It assesses how well the relationship between the variables can be described by a monotonic function, either increasing or decreasing.

Calculation involves ranking the data: replace each observation with its rank within its variable. If ties occur, ties are averaged or corrected. The coefficient is the Pearson correlation between the two sets of ranks: ρ_s = corr(R_x, R_y). In the standard no-ties case, ρ_s = 1 − 6 ∑ d_i^2 / [n(n^2 − 1)], where d_i are the differences between paired ranks. A tie-adjusted form generalizes this using ranks with weights.

Range is from −1 to +1. Values near +1 indicate a strong increasing monotonic relationship, values near −1 indicate a strong decreasing monotonic relationship, and values near 0 indicate little or no monotonic association. The method is robust to outliers and does not assume linearity or normality.

SpearmanKorrelation differs from Pearson correlation, which measures linear correlation and assumes interval data and normality. Spearman focuses on monotonic relationships and is appropriate for ordinal data or continuous data that violate parametric assumptions.

Applications include psychology, biology, economics, and data science, where researchers seek to detect monotonic associations, perform feature selection, or analyze nonparametric relationships. The coefficient was introduced by Charles Spearman in the early 20th century.