In statistics, the Shapiro–Wilk test tests the null hypothesis that a sample x1, ..., xn came from a normally distributed population. It was published in 1965 by Samuel Shapiro and Martin Wilk.[1]
The test statistic is:
where
The user may reject the null hypothesis if W is too small.[3]
It can be interpreted via a Q-Q plot.
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Recalling that the null hypothesis is that the population is normally distributed, if the p-value is less than the chosen alpha level, then the null hypothesis is rejected (i.e. one concludes the data are not from a normally distributed population). If the p-value is greater than the chosen alpha level, then one does not reject the null hypothesis that the data came from a normally distributed population. E.g. for an alpha level of 0.05, a data set with a p-value of 0.32 does not result in rejection of the hypothesis that the data are from a normally distributed population.[1]
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