I have carried out a chi-squared test in an 11x4 table with a sample of c. 11,000 units.
I've got a very high chi-squared value (x2=9807; df=30) and the p-value is extremely low (p=2.2e-16), which I know it's expected because of the size of the sample size.
To check whether this can be biased by sample size, I have also calculated Cramer's V effect size, which gives a result of 0.56 (which means that there is a moderate association between variables).
Since the aim is to check whether there is a preference for a particular 'Type' to express each 'Pattern', I have calculated Pearson residuals.
So, my questions are: i) Is x2 and df too large to be reliable? ii) Since Cramer'V reports a moderate association, does it mean chi can be used? iii) Is it ok to use Pearson residuals with complex tables and large samples like this one?