# Large chi-squared value

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?

Thank you!

• As dimensionality of table increases, so does DF, and also value of chi-sq statistic, even if $H_0$ true. You show a limited number of Pearson residuals. With such a large chi-sq stat it seems reasonable to have at least a few residuals so large. // You have not shown much, but I see no red flags in the little you have shown. Commented May 17, 2022 at 13:35

None of these things are relevant;

(i) the size of the df and the chi-squared will of themselves tell you nothing about the suitability/reliability of what you did (however you define reliability).

(ii) the specific value of Cramer's V will (of itself) tell you nothing about the suitability of what you did (whether it's near 0 or near 1, or somewhere in between)

(iii) The large size of the table indicate nothing about the suitability of using Pearson's residuals. If anything they may be slightly easier to interpret in a larger table since they'll be less dependent, but they'll still be potentially useful in small tables.

The properties of these things all relate to very different considerations than the issues you raise. None of the things you ask about imply any problem, nor do they imply that everything is fine, they're all incidental features for such concerns -- in a similar way that the size of a car's interior is not of itself an indication of whether the car needs fuel.

• Ok, I see! Thank you for your comment!
– user358390
Commented May 19, 2022 at 8:22