Cohen's Kappa Statistic/Examples/Medical Diagnosis

Example of Use of Cohen's Kappa Statistic

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:

$\kappa = 0 \cdotp 675$

Here we have:

$\ds N$

$=$

$\ds 80$

$\ds n$

$=$

$\ds 32 + 35 = 67$

$\ds \leadsto \ \ $

$\ds p_{\mathrm {obs} }$

$=$

$\ds \dfrac n N = 0 \cdotp 8375$

$\ds p_{\mathrm {exp} }$

$=$

$\ds \dfrac {40} {80} = 0 \cdotp 5$

$\ds \leadsto \ \ $

$\ds \kappa$

$=$

$\ds \dfrac {p_{\mathrm {obs} } - p_{\mathrm {exp} } } {1 - p_{\mathrm {exp} } }$

$\ds $

$=$

$\ds \dfrac {0 \cdotp 8375 - 0 \cdotp 5} {1 - 0 \cdotp 5}$

$\ds $

$=$

$\ds 0 \cdotp 675$

$\blacksquare$