It's well established that both Anderson-Darling and Shapiro-Wilk have a much higher power to detect departures from normality than a KS-Test.
I have been told that Shapiro-Wilk is usually the best test to use if you want to test if a distribution is normal because it has one of the highest powers to detect lack of normality, but my limited experience, it seems that Shapiro-Wilk gives me the same result as Anderson-Darling every time.
I thus have two questions:
- When does the Shapiro-Wilk test out-perform Anderson-Darling?
- Is there a uniformly most powerful lack of normality test, or, barring that possibility, a normality test that out-performs nearly all other normality tests, or is Shapiro-Wilk the best bet?