Somers Concordance Statistic

Definition

Somer's D Statistic is a measure of association for ordinal variables. It is based on comparing the value of two variables for all possible instances of associated pairs.

Preliminaries

An pair of observed instances (x1, y1), (x2, y2) can be:

• Concordant, if the values of both variables for one case are higher (or lower) than the corresponding values for the other instances.
• Discordant, if the value of one variable for one instance is higher than the corresponding value for the other instance, and vice-verse

for the other variable.

• Tied, if the two instances have the same value on one or on both

variables.

Formula

$D = \frac{P - Q}{P + Q + T}$

Where P is the count of concordant instances, Q is the count of discordant instances and T is the count of tied instances

See Also

• Gamma Statistic