In statistics, Cohen’s Kappa is used to measure the level of agreement between two raters or judges who each classify items into mutually exclusive categories.
The formula for Cohen’s kappa is calculated as:
k = (po – pe) / (1 – pe)
- po: Relative observed agreement among raters
- pe: Hypothetical probability of chance agreement
Rather than just calculating the percentage of items that the raters agree on, Cohen’s Kappa attempts to account for the fact that the raters may happen to agree on some items purely by chance.
The value for Cohen’s Kappa always ranges between 0 and 1where:
- 0 indicates no agreement between the two raters
- 1 indicates perfect agreement between the two raters
The following table summarizes how to interpret different values for Cohen’s Kappa:
The following example shows how to calculate Cohen’s Kappa in Python.
Example: Calculating Cohen’s Kappa in Python
Suppose two art museum curators are asked to rate 15 paintings on whether they’re good enough to be shown in a new exhibit.
The following code shows how to use the cohen_kappa_score() function from the sklearn library to calculate Cohen’s Kappa for the two raters:
from sklearn.metrics import cohen_kappa_score #define array of ratings for both raters rater1 = [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0] rater2 = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0] #calculate Cohen's Kappa cohen_kappa_score(rater1, rater2) 0.33628318584070793
Cohen’s Kappa turns out to be 0.33628.
Based on the table from earlier, we would say that the two raters only had a “fair” level of agreement.
If you want to calculate the level of agreement between three or more raters, it’s recommended to use Fleiss’ Kappa instead.
You can use the fleiss_kappa() function from the statsmodels library to calculate this metric.
Note: You can find the complete documentation for the cohen_kappa_score() function here.
The following tutorials offer additional resources on Cohen’s Kappa:
Introduction to Cohen’s Kappa
How to Calculate Cohen’s Kappa in Excel
Cohen’s Kappa Calculator