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- Is normality testing 'essentially useless'? 16 answers
When I read research papers, I saw that many people do a normality test first, then decide if a t-test or a non-parametric test should be applied.
I have a concern about such practice. Let’s say the sample follows a gamma distribution, which is kind of bell shaped, but different from normal. The larger the sample size, the more power the normality test has. So a big sample size can lead to the rejection of normality. On the other hand, the larger the sample size, the better fit with central limit theorem. As a result, even though the sample is not normal, its mean can be approximated by normal.
So we have a paradox: on one hand, large sample means its mean can be approximated by normal, which means t-test can be applied.
on the other hand, large sample give normality test more power, which in turn rejects the use of t test.
Is my concern valid? Why people do normality test? Is there an alternative way?