This is more of a theoretical question. Super large sample sizes will almost always show a significance when a $\chi^2$ test is done. Is there any other statistical test of significance (an alternative to $\chi^2$) which is good for testing independence when the sample size is very large?
This is the context of my problem: I have 2 large datasets of phrases. Set1 corresponds to the Google n-grams set and set2 is a smaller set corresponding to the phrases found in one single website. Now consider a phrase: say ('Technology') found in Set2. I want to test and see if this phrase is specific to this website (it could be if it is a Technology website) or if it is a general phrase. So I am performing a $\chi^2$ test between the frequency of phrases in the two sets as follows:
Set1 Set2 Not_Technology (set1) 2,674,797,869,255 (set2) 46,168,477.00 Technology (set1) 1710231 (set2) 1991
I understand that this might not be the best method to test whether a phrase is a general phrase or not, so if you have any suggestions or criticisms I am happy to listen to them.