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I have a dataset with labels and usernames:

Labels   Usernames
1         Londonderry
1         Londoncalling
1          Steveonder43
0         Maryclare_re
1         Patent107391
0         Anonymous 
1         _24londonqr
... 

It seems that the usernames containing the word London are very frequent in having assigned label=1. Do you have any idea on how I could proof it?

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You could create a second label for your usernames according to whether they contain london or not (pseudocode below):

for idx, username in df['Usernames']:
    if 'London' in username:
        df['London'].iloc[idx] = 1
    else:
        df['London'].iloc[idx] = 0

Consequently given you want to go with correlation and that you are comparing binary variables, the metric to go with is Pearson correlation coefficient (pseudocode below):

import scipy.stats.pearsonr as rho
corr = rho(df['labels'], df['London'])
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