Chi-square test of independence of 2 variables on a large sample Is it safe to check the Chi-square test of independence with a sample of 25000 ?
I have the answers of approximately 25.000 people of different countries, as frequencies (total sums for each question). They asked to evaluate a threat based on their perception from 1 to 10 (1: non existent, 10: extremely high) and to reply to some demographics. 
Now i want to check if sex (male, female) correlates with the perception of the evaluation, and secondly if it does, how strong it is.
I read that this test is not safe when the sample is very big (n>250) because then there is a possibility the statistical importance of the relationship of the 2 variables to be “fictive” cause of the overgrowing of the value of chi square.
Unfortunately is not available to quote because it’s not in English.
 A: First, if one variable is a count you might want to use something other than chi-square. Perhaps a t-test or Mann Whitney U. It depends on exactly what you want to check.
Second, I think I can see what the article is talking about. But it's not a question of chi-square (or any test) being "safe" with large N - that looks like some sort of mistranslation. It is true that, with large N, a statistically significant difference may be of no practical importance. If you find a small p with the test, it means the same thing as it always does: If the null (independence) were true in the population, then you'd be unlikely to get a test statistic (chi-square) at least as extreme as the one you got in a sample the size of the one you have.
However, you can also look at the degree to which the null is wrong. Here, how far from equal are the distributions?  The crosstabulation (and associated percentages) will let you get a sense of that. 
A: There are different aspects to consider. 


*

*Approximate tests (like the one you are using) tend to provide more accurate p-values for large samples. So you are fine.

*The power of a test, i.e. its ability to detect a true working hypothesis, tends to increase with larger sample size. Eventually, even small effects can yield small p values. This is not a problem of the test but is related to the third aspect:

*The "default" working hypothesis of a test (e.g. there is a relation between the two variables, no matter how small) is often not very interesting. This can easily be mended by asking more relevant questions. So instead of asking "Is there any true association?" you could ask "Is the true association at least weak?" (e.g. in terms of the population Cramèr's V or population Spearman's rank correlation being larger than a certain threshold in absolute value). 
(Combining 2. and 3. we can say that large sample sizes allow us to answer interesting questions.)
