Central limit theorem #39
Description
Course materials could be more nuanced with respect to how/when the CLT can be "used" to relax the assumption of normality
Specifically - it's an asymptotic result, and when there are very large departures from normality, even a massive sample size won't help. Realistically, the bigger the deviation from normality the larger your sample needs to be, and beyond a certain point even huge data won't "fix" the problem
Also think the literature cut off of n>30 being "big" is far too liberal!
Suggest revising the materials to go with a more nuanced view:
We can get away with some deviations away from normality in larger samples due to the central limit theorem, but if the residuals are very clearly non-normal (very clearly following some other distribution, rather than just being a bit leptokurtic or skewed), CLT shouldn't be used to justify ignoring an important assumption