In statistics, Somers’ ''D'', sometimes incorrectly referred to as Somer’s ''D'', is a measure of
ordinal association
In statistics, a rank correlation is any of several statistics that measure an ordinal association — the relationship between rankings of different ordinal variables or different rankings of the same variable, where a "ranking" is the assignment ...
between two possibly dependent random variables and . Somers’ ''D'' takes values between
when all pairs of the variables disagree and
when all pairs of the variables agree. Somers’ ''D'' is named after Robert H. Somers, who proposed it in 1962.
Somers’ ''D'' plays a central role in rank statistics and is the parameter behind many nonparametric methods.
It is also used as a quality measure of
binary choice or
ordinal regression
In statistics, ordinal regression, also called ordinal classification, is a type of regression analysis used for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where only the relative ordering between di ...
(e.g.,
logistic regression
In statistics, a logistic model (or logit model) is a statistical model that models the logit, log-odds of an event as a linear function (calculus), linear combination of one or more independent variables. In regression analysis, logistic regres ...
s) and
credit scoring
A credit score is a numerical expression based on a level analysis of a person's credit files, to represent the creditworthiness of an individual. A credit score is primarily based on a credit report, information typically sourced from credit bur ...
models.
Somers’ ''D'' for sample
We say that two pairs
and
are
concordant
Concordance may refer to:
* Agreement (linguistics), a form of cross-reference between different parts of a sentence or phrase
* Bible concordance, an alphabetical listing of terms in the Bible
* Concordant coastline, in geology, where beds, or la ...
if the ranks of both elements agree, or
and
or if