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In statistics, the Shapiro-Wilk test tests the null hypothesis that a sample x_{1}, ..., x_{n} came from a normally distributed population. The test statistic is
where
- x_{(i)} (with parentheses enclosing the subscript index i) is the ith order statistic, i.e., the ith-smallest number in the sample;
- is the sample mean;
- the constants a_{i} are given by
- where
- and m_{1}, ..., m_{n} are the expected values of the order statistics of an iid sample from the standard normal distribution, and V is the covariance matrix of those order statistics.
The test rejects the null hypothesis if W is too small.
ReferencesEdit
- Shapiro, S. S. and Wilk, M. B. (1965). "An analysis of variance test for normality (complete samples)", Biometrika, 52, 3 and 4, pages 591-611.
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