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I consider the next piece of code

library(UsingR)
data(babies)

hist(babies$wt)
shapiro.test(babies$wt)

enter image description here

As you can see the data seems perfectly normally distributed, moreover the sample size seems to be good enough > 1000 individuals.

However, the results of the Shapiro Wilks test have different results.

  data:  babies$wt
  W = 0.99559, p-value = 0.001192

Why it is happening?? I can not understand this phenomena.

Dave
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Boris
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    Does this answer your question? Is normality testing 'essentially useless'? // Also… – Dave Jul 26 '22 at 23:26
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    You hint at a common misconception about the central limit theorem by mentioning the large sample size of a thousand (as if having a thousand points means that your data should converge toward a normal distribution). – Dave Jul 26 '22 at 23:28
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  • The distribution doesn't look quite normal to me; the peak looks too narrow and the tails slightly on the thicker side, but histograms can be misleading. It's symmetric and unimodal but lots of distributions are symmetric and unimodal.$:$ 2. With a large sample, you can detect even trivial deviations from normality. What value is there in testing it? Clearly weights cannot actually be normally distributed (for all that it might be an excellent and useful approximation). The test doesn't tell you whether normality is close enough for some purpose. What can it tell you that you don't know?
    • – Glen_b Jul 27 '22 at 00:21