Understanding Cohen’s Kappa Score With Hands-On Implementation

In this article, we will learn in detail about what Cohen’s kappa is and how it can be useful in machine learning problems.

After a machine learning model is trained and tested, there are two primary factors that need attention. These are reliability and validity. Reliability is the level of trust we have on the model to produce consistent results in similar situations. It is the precision of the model. On the other hand, validity is the accuracy of the model on test data, that is how good is the result produced. 

Cohen’s Kappa is a statistical measure that is used to measure the reliability of two raters who are rating the same quantity and identifies how frequently the raters are in agreement. 

In this article, we will learn in detail about what Cohen’s kappa is and how it can be useful in machine learning problems.


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Intra-rater and inter-rater reliability

Before we understand Cohen’s Kappa, let us understand what Intra and inter-rater reliability are. Consider an experiment where two people are voting yes or no. 

Intra-rater reliability is when the same type of experiment is completed by the same rater but in two or more different situations.

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Inter-rater reliability is when there are two different raters who are rating for the same experiment and they agree on the same vote. 


Understanding and evaluating Cohen’s Kappa

If there are N items that need to be classified into C mutually exclusive categories, the work of Cohen’s kappa is to measure the agreement between the two raters in order to classify N to C. 

The value for this can be between 0 and 1 where 0 means there is no or random agreement between the raters and 1 indicates there is total agreement between them. But there can even be a negative value which indicates that there is absolutely no agreement between them. 

To make things simple, let us derive the formula and make calculations to evaluate this metric. 

Assume there are two raters r1 and r2 and they are rating ‘yes’ and ‘no’. Their choices are as follows:



Now I will make a grid that can calculate the number of yeses and no’s.

R2 yesR2 no
R1 yes41
R1 no22

Now, let us make the calculations

First, let us calculate the total possibilities in which both parties agree. That is the diagonal of the above matrix.

Agreement= sum of agreements / total number of instances

Agreement = (4+2)/9 = 0.66

Now we need to consider the cases where raters are not in agreement. We will do this calculating probability of yes and no.

p(yes)= ((4+1)/9)*((4+2)/9)=0.37


Total non disagreement= 0.37+0.14= 0.51

To calculate the Kappa coefficient we will take the probability of agreement minus the probability of disagreement divided by 1 minus the probability of disagreement. 

cohens kappa

K= 1-(0.34/0.49) = 0.31

This is a positive value which means there is some mutual agreement between the parties. 

Let us now implement this with sklearn and check the value. 



from sklearn.metrics import cohen_kappa_score


Special cases:

  1. When there are opposing votes the value of k is 0 which means there is no agreement between the parties. 



from sklearn.metrics import cohen_kappa_score


  1. When there are very few agreements between the two the k value is negative



from sklearn.metrics import cohen_kappa_score


The main use of Cohen’s kappa is to understand and identify if the data that is collected for training purposes is the correct representation of variables or not. If the values are closer to 1 it is considered good and values closer to 0 are uncertain. 


In this article, we understood the complete working of Cohen’s kappa and made the calculations as well. With this information, it can be useful in understanding the data distribution and which values are reliable and which are not.

The complete code of the above implementation is available at the AIM’s GitHub repository. Please visit this link to find the notebook of this code.

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Bhoomika Madhukar
I am an aspiring data scientist with a passion for teaching. I am a computer science graduate from Dayananda Sagar Institute. I have experience in building models in deep learning and reinforcement learning. My goal is to use AI in the field of education to make learning meaningful for everyone.

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