Symmetric and directional measures

Symmetric and directional measures of ordinal association are based on the idea of accounting for concordance versus discordance. Each pairwise comparison of cases is classified as one of the following.

• A pairwise comparison is considered concordant if the case with the larger value in the row variable also has the larger value in the column variable. Concordance implies a positive association between the row and column variables.
• A pairwise comparison is considered discordant if the case with the larger value in the row variable has the smaller value in the column variable. Discordance implies a negative association between the row and column variables.
• A pairwise comparison is considered tied on one variable if the two cases take the same value on the row variable, but different values on the column variable (or vice versa). Being tied on one variable implies a weakened association between the row and column variables.
• A pairwise comparison is considered tied if the two cases take the same value on both the row and column variables. Being tied implies nothing about the association between the variables.

The measures differ in how they treat each type of comparison.

Next