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, Lilliefors and Anderson–Darling tests. 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. 05 rejects the null hypothesis that the data are from a normally distributed population). 05, a data set with a p value of less than. On the other hand, if the p value is greater than the chosen alpha level, then the null hypothesis (that the data came from a normally distributed population) can not be rejected (e.g., for an alpha level of. Thus, 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. The null-hypothesis of this test is that the population is normally distributed. The cutoff values for the statistics are calculated through Monte Carlo simulations.
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W = ( ∑ i = 1 n a i x ( i ) ) 2 ∑ i = 1 n ( x i − x ¯ ) 2. , x n came from a normally distributed population.
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The Shapiro–Wilk test tests the null hypothesis that a sample x 1.