Definition:Cohen's Kappa Statistic
Definition
Let two observers $A$ and $B$ independently classify each of a set of observations into $2$ or more categories.
Cohen's kappa statistic $\kappa$ is a measure of agreement between $A$ and $B$.
Let there be $N$ observations.
Let $n$ denote the number of agreements over all categories.
Let $p_{\mathrm {obs} } := \dfrac n N$ be the observed proportion of agreements.
Let $p_{\mathrm {exp} }$ denote the expected proportion of agreements over all categories under random assignment, as calculated in the usual manner for a contingency table.
Then:
- $\kappa = \dfrac {p_{\mathrm {obs} } - p_{\mathrm {exp} } } {1 - p_{\mathrm {exp} } }$
Examples
Medical Diagnosis
Let there be $80$ patients claiming to suffer from depression
Let there be $2$ doctors who are to assess whether or not it is appropriate to treat each patient with a particular antidepressant drug.
In $32$ cases, both agree that treatment is appropriate.
In $35$ cases, both agree that treatment is not appropriate.
In the remaining $13$ cases, they disagree: one doctor believes treatment is appropriate, while the other does not.
Then Cohen's kappa statistic $\kappa$ is evaluated to be:
- $\kappa = 0 \cdotp 675$
Also known as
Cohen's kappa statistic is also known as:
Also see
- Results about Cohen's kappa statistic can be found here.
Source of Name
This entry was named for Jacob Cohen.
Historical Note
Cohen's kappa statistic was devised by Jacob Cohen in $1960$.
Linguistic Note
The kappa in the name of Cohen's kappa statistic is the Greek letter $\kappa$ which is used to denote it.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cohen's kappa statistic