Rank Correlation - General Correlation Coefficient

General Correlation Coefficient

Kendall (1944) showed that his tau and Spearman's rho are particular cases of a general correlation coefficient.

Suppose we have a set of objects, which are being considered in relation to two properties, represented by and, forming the sets of values and . To any pair of individuals, say the -th and the -th we assign a -score, denoted by, and a -score, denoted by . The only requirement made to this functions is anti-symmetry, so and . Then the generalised correlation coefficient is defined by