are given by:[1] where C is a vector norm:[2] and the vector m, is made of the expected values of the order statistics of independent and identically distributed random variables sampled from the standard normal distribution; finally,
If the p value is less than the chosen alpha level, then the null hypothesis is rejected and there is evidence that the data tested are not normally distributed.
[4] Like most statistical significance tests, if the sample size is sufficiently large this test may detect even trivial departures from the null hypothesis (i.e., although there may be some statistically significant effect, it may be too small to be of any practical significance); thus, additional investigation of the effect size is typically advisable, e.g., a Q–Q plot in this case.
[5] Monte Carlo simulation has found that Shapiro–Wilk has the best power for a given significance, followed closely by Anderson–Darling when comparing the Shapiro–Wilk, Kolmogorov–Smirnov, and Lilliefors.
[7] This technique is used in several software packages including GraphPad Prism, Stata,[8][9] SPSS and SAS.