如何在2x2矩阵上应用Cramer V

Question

I want to find the association between variables and cramer V works like a treat for matrices of sizes greater than 2X2. However, for matrices with low frequencies, it does not work well. For the following contingency matrix, i get the result as 0.5. How can I account for the same?

  1 2  
a 2 0  
b 0 2  

Here is my code:

def cramers_stat(confusion_matrix):  
    chi2 = ss.chi2_contingency(confusion_matrix)[0]  
    n = confusion_matrix.sum().sum()  
    return np.sqrt(chi2 / (n*(min(confusion_matrix.shape)-1)))  
result=cramers_stat(confusion_matrix)  
print(result) 

confusion_matrix is my input, in this case the matrix i mentioned above. I understand for good results, i need a matrix frequency above 5, but for perfect association as the case above I expected the result to be 1.

Answer 1

When you compute the Cramér coefficient, you must compute chi2 without continuity correction . For a 2x2 matrix, chi2_contingency uses continuity correction by default. So you must tell chi2_contingency to not use continuity correction by giving the argument correction=False :

chi2 = ss.chi2_contingency(confusion_matrix, correction=False)[0]