# Checking the normality of a large sample?

If I want to analyze a large sample size (N = 50.000) of continuous data (\$ revenue) from an A/B test, what would then be the best way to check for normality?

• Why do you want to check for normality? Dec 25, 2019 at 10:27
• to understand if I can use for example a T-test or if I need to use something like a mann-whitney u test Dec 25, 2019 at 10:30
• The t test does not require that the observations are normally distributed; it requires that the means are. By the Central Limit Theorem, they are so asymptotically even if the original observations have a quite non-normal distribution, under some quite weak assumptions. The Mann-Whitney test is nonparametric and makes no normality assumptions. You can probably use a t test out of the box, or possibly consider a permutation test for means (but see here). Dec 25, 2019 at 10:41
• That the numerator in a t-test is close to normal is not of itself sufficient to make a t-statistic have a t-distribution. To get that, you really do need the observations to be normal. Beyond that, in large samples you have a justification for an approximate z-test (CLT + Slutsky), not a t-test. Is there some argument that shows that t will be better than z in general in that situation? Dec 25, 2019 at 11:42