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In this Stackoverflow answer Ian Fellows said,

Normality tests don't do what most think they do. Shapiro's test, Anderson Darling, and others are null hypothesis tests AGAINST the the assumption of normality. These should not be used to determine whether to use normal theory statistical procedures. In fact they are of virtually no value to the data analyst. Under what conditions are we interested in rejecting the null hypothesis that the data are normally distributed? I have never come across a situation where a normal test is the right thing to do.

But if we reject the null, it tells us that the data is not normally distributed - isn't that a piece of information that could be helpful - which gives us a reason to use these tests? Can that be a reason to use these normality tests?

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marked as duplicate by Nick Cox, Glen_b hypothesis-testing Apr 7 at 11:16

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  • $\begingroup$ If this has been aired on SO, expect that it has aired even more frequently here. $\endgroup$ – Nick Cox Apr 7 at 11:15