Is an F-test for equality of variance appropriate for a very large dataset? I have a dataset with about 500,000 subjects and I am trying to establish whether the variance is equal. I first performed an F-test but then I realised the data is slightly skewed with kurtosis. So then I went with the  Brown-Forsythe variation of the Levene test of variance because it utilises the median and thus is less influenced by non-normality in the data. Then I realised that, due to the central limit theorem, if the sample is sufficiently large, then one can treat the data as normally distributed.
So now I am torn. Do I perform the F-test or the Levene's test? Or is there a better test to carry out on data this size?  
 A: A-priori, I find it highly implausible that the variances would be exactly equal (meaning that the null hypothesis should not be rejected, even with very high $n$ as you have here).  As a result, I do not see what purpose is served by testing for heteroscedasticity*.  
Assuming one prefers to use a $t$-test (to, say, the Mann-Whitney $U$-test), when heteroscedasticity exists, using the Welch correction may be appropriate.  However, given that the ratio of variances is $1.072037$, and $N = 500,\!000$, I can't see that it matters much either way.  I don't think the validity of the non-Welch-corrected $t$-test is threatened by heteroscedasticity so small, and I suspect the Welch $t$ would be virtually identical to the standard $t$ with that $N$.  
* To understand this topic more thoroughly, it may help to read these two excellent CV threads:
  1. Is normality testing 'essentially useless'?
  2. A principled method for choosing between t test or non-parametric e.g. Wilcoxon in small samples.
