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.