Spearmans

Spearmans refers to terms named after Charles Spearman and, more broadly, to his methodological legacy in statistics and psychology. The best known is Spearman's rank correlation coefficient, commonly called Spearman's rho, used to assess monotonic relationships between two variables. Charles Spearman (1863–1945) was a British psychologist who helped develop factor analysis ideas and argued for a general intelligence factor, "g".

Spearman's rho measures how well the relationship between two variables can be described by a monotonic function. The data are first converted to ranks, and the correlation of the ranks is computed. For data without tied ranks, the coefficient can be written as rho = 1 − 6 Σ d_i^2 / [n(n^2 − 1)], where d_i is the difference between the ranks of paired observations. If ties are present, ranks are averaged and a tie-corrected form is used; in practice, Spearman's rho is equivalent to the Pearson correlation of the ranked variables and always falls in the interval −1 to 1.

Uses and interpretation: appropriate for ordinal data or nonparametric contexts; robust to outliers and non-linear but monotonic relationships. It is widely used in psychology, education, and the social sciences, as well as in biomedical and market research when the data do not meet the assumptions of Pearson correlation.

Other references to Spearman in science include his contributions to intelligence theory and his influence on nonparametric statistics. In common usage, "Spearmans" may refer to things named after Spearman or to individuals bearing the surname Spearman.