How to Calculate Cohen's Kappa Index Value - Tutorial

How to Calculate Cohen's Kappa Index Value - Definition, Formula, Example

Definition:

Cohen's kappa coefficient is a numerical evaluation of inter-rater agreement or inter-annotator agreement for categorical entries.

Formula:

k = (Pr(a) - Pr(e)) / (1-Pr(e)) Where, Pr(a) - Relative observed agreement, Pr(e) - Hypothetical probability of chance agreement, k - Cohen's kappa index value
Example:

20 patients are examined by two independent doctors.'Yes' denotes that the patients are diagnosed with disease X by a doctor.'No' denotes that the patients are classified as no disease X by a doctor.

  Doctor A  
  Yes No Total
Doctor B Yes 12 2 14 ( 70 %)
No 4 2 6 ( 30 %)
Total 16 ( 80 %) 4 ( 20 %) 20
Solution:

Substitute the given values in the formula,
k = ( Pr (a) - Pr (e) ) / ( 1 - Pr (e) ) Pr(a) = ( 12 + 2 ) / 20 = 0.7 Pr(e) = ( 0.7 * 0.8 ) + ( 0.2 * 0.3 ) = 0.62 k = ( 0.7 - 0.62 ) / ( 1 - 0.62 ) = 0.08 / 0.38 k = 0.21

Hence the Cohen's kappa index value is calculated.

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