I am trying to find if there is a correlation between the two categorical variables (Var1 and Var2). For that I am performing Cramer's V test on the RxC contingency table since the test that gives the p-value is insufficient as it is dependent on the population size.
Having obtained the Cramer's value, I want to know specifically which labels (1,2,3,..M..N) taken from both variables correlate the most.
I have found that I can do a chi2 test to find if different rows or columns have some correlation (https://www.bmj.com/about-bmj/resources-readers/publications/statistics-square-one/8-chi-squared-tests)
Now I would like to find cell-wise correlations. The first thing I thought about was performing a test of whether Var1.labelN+Var2.labelM have strong or weak correlation in the population. For that I have thought about extracting 'local' 2x2 contingency table from the overall RxC contingency table and performing Cramer's V test on the local table. Below is the picture on how I am extracting the local contingency table.
The null hypothesis with the local contingency table would be that "in the taken population there is no correlation between Var1.label M and Var2.label N"
If the data would have been evenly distributed, I could have just use the likelihood (odds) test to verify or reject the null hypothesis, but in my case the data is very unbalanced
Could anyone tell me if such approach makes sense?