Apologies for the basic question this is really not my area at all but I’m trying to help a friend out.
Whilst reading the Wikipedia page for the Shapiro-Wilk test I came across the following: “As with most statistical tests, the test may be statistically significant from a normal distribution in any large samples. Thus a Q–Q plot is useful for verification in addition to the test”
I interpret this to mean that if we sampled a large amount of data from what was in fact a Normal population, the test may in fact reject the null hypothesis that the parent population was Normal. Is this interpretation correct?
If so, why is this the case? I thought in general larger samples gave better testing?! Any intuition on this would be very much appreciated.