Coefficients for Bivariate Relations

A bivariate relation is a relation between two (X and Y) variables. A large number of coefficients for bivariate relations was developed. A classification of coefficients is presented to facilitate the choice of an appropriate coefficient. The classification is based on two distinctions. First, three types of relations are distinguished: (1) symmetrical (the relation between X and Y is the same as between Y and X), (2) equality (symmetrical and equality of X- and Y-values), and (3) asymmetrical (one variable is the independent variable or predictor and the other variable is the dependent variable or criterion). Second, five types of variables are distinguished: (1) dichotomous (two unordered or ordered categories), (2) nominal-categorical (more than two unordered categories), (3) ordinal-categorical (more than two ordered categories), (4) ranked (rank numbers), and (5) continuous (values from a continuum). Crossing of these two distinctions yields 3 × 5 = 15 different combinations. An example of a coefficient is given for 13 of these combinations (coefficients for the two other combinations are not known to the author). The examples are restricted to coefficients for relations between two variables of similar type, for example, Cohen’s kappa for an equality relation between two nominal-categorical variables.