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Shapiro-Wilks Normality Test

The Shapiro-Wilks test for normality is one of three general normality tests designed to detect all departures from normality.  It is comparable in power to the other two tests.

The test rejects the hypothesis of normality when the p-value is less than or equal to 0.05.  Failing the normality test allows you to state with 95% confidence the data does not fit the normal distribution.  Passing the normality test only allows you to state no significant departure from normality was found.

The Shapiro-Wilks test is not as affected by ties as the Anderson-Darling test, but is still affected.  The Skewness-Kurtosis All test is not affected by ties and thus the default test.