Correcting Cramer's V

[oualib]

This PR corrects the computation of Cramer's V.
TODO:

• optimise the corr code.

[oualib]

@vikash018 you might need to update correlation tests for Cramer's V.

To compute it using Python:

import scipy.stats as ss
import numpy as np

def cramers_corrected_stat(confusion_matrix):
    """ calculate Cramers V statistic for categorial-categorial association.
        uses correction from Bergsma and Wicher, 
        Journal of the Korean Statistical Society 42 (2013): 323-328
    """
    chi2 = ss.chi2_contingency(confusion_matrix)[0]
    n = confusion_matrix.sum().sum()
    phi2 = chi2/n
    r,k = confusion_matrix.shape
    phi2corr = max(0, phi2 - ((k-1)*(r-1))/(n-1))    
    rcorr = r - ((r-1)**2)/(n-1)
    kcorr = k - ((k-1)**2)/(n-1)
    return np.sqrt(phi2corr / min( (kcorr-1), (rcorr-1)))

import pandas as pd

df = vpd.load_titanic().to_pandas() # taking a dataset
confusion_matrix = pd.crosstab(df["pclass"], df["age"])

cramers_corrected_stat(confusion_matrix)

Result: 0.2940639041452328

Same for VerticaPy.

 vpd.load_titanic().corr(["pclass", "age"], method="cramer")

You can take multiple examples.