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If we get a p-value for both the Shapiro-Wilk test and Anderson-Darling test greater than 0.05 for all samples that I have for example(100 samples), but the p-value for the Shapiro-Wilk test are greater than the p-value for and Anderson-Darling, in this case, how can we interpret the p-value for the Shapiro-Wilk test, can we say the Shapiro-Wilk test is best according to that.

Statistical scientist
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  • Its not a matter of best. Shapiro wilk test is usef to test normality. If we reject then the data is not normal. In your case since you do not reject we can assume that the data is normaly dustributed. I am not farmiliar with the Anderson-Darling. But if it is also usef to test normality, we would still not reject, thus both tests giving the same conclusion. Note that these tests are frequentist way of determining as to whether it is safe to assume normality. Its not a matter of which test is best – KU99 Dec 18 '21 at 08:01
  • S-W and A-D are often listed among the most powerful normality tests (that is, most likely properly to detect non-normality). Read about the pros and cons of various normality tests, pick your favorite, and see what it says. Don't do multiple tests on the same data. // Maybe most important, look at a normal probability plot (Q-Q plots), to see whether data points seem to lie along a straight line (except for maybe a relatively few in the tails). – BruceET Dec 18 '21 at 13:28
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    Normality is a matter of degree. Making an all-or-nothing decision about normality is a recipe for downstream problems. – Frank Harrell Dec 18 '21 at 13:44

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