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I know that as the sample size increases, the sampling distribution of the mean will become normally distributed, even if the population data are skewed (non-normal). So we can safely assume that the sampling distribution of the mean will be fairly normal.

However, I was wondering what happens if the shape of the sampling distribution is somehow non-normal (it might be oblivious to us) and its associated SEM? Is the SEM going to be misleading for calculating the confidence intervals and significance testing?

e. erhan
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  • Please give an example of a sampling distribution that is non-normal. It seems to me you might be talking about small-sample sampling distributions. – Gregg H Jan 16 '21 at 16:09
  • @GreggH Some kind of infinite variance distribution? – Dave Jan 16 '21 at 16:35
  • @GreggH yes, I have been mainly thinking about small-sample sampling distributions – e. erhan Jan 16 '21 at 19:11
  • @e.erhan ¿are you considering distributions with undefined (infinite) variance? – Gregg H Jan 16 '21 at 19:39
  • is this what you are asking? https://stats.stackexchange.com/questions/105337/asymptotic-distribution-of-sample-variance-of-non-normal-sample – ma83 Jan 16 '21 at 20:55
  • @M.Austin this link answers my question (I suppose, but I will read it in detail). thanks! – e. erhan Jan 17 '21 at 15:30

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