Using chi-squared test for goodness of fit for different sizes of sample?

Firstly, apologies if I'm posting this in completely the wrong place.

I'm trying to figure out a way to allow for different sized samples when doing a chi-squared test for goodness of fit.

The degrees of freedom are always the same (11) as I'm trying to test whether a sample of births are spread evenly over the year or not.

My samples range from 23 to 300, but to give an extreme example, for UK births in 2009 the chi-squared statistic is 376.3 (sample size of 706,200) for all UK births from 1985 to 2002 it's 5827.9 (sample size of 11.7 million) and for all USA births for same period it's 27587.4 (with a sample size of 31.68 million)

So if the chi squared statistic gets bigger as the sample size gets bigger, how can I be sure that my results are as accurate for the larger samples as they are for the smaller samples, as the only guidance I can find is that the expected value has to be greater than 5?

Thanks in advance for any help you can offer.


No cake for spunky
Chi square is heavily influenced by sample size (I believe it inflates with sample size). That is a signficant, and well known, limitation of the method.

As far as I know there is no method to correct for this (that is somehow standardize the chi square for sample size). If there was it would be done already (notably in SEM where inflation of chi square is a signficant issue with goodness of fit indicators).

You simply report your n and chi square and let your audience decide.