Standard Statistical Tests for Normality:
The Shapiro-Wilk test
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See also Standard Statistical
Tests for Normality.
The Shapiro-Wilk test tests the null hypothesis that
a sample, 
comes
from a Normally distributed population.
It was published in 1965, see Shapiro and
Wilk (1965), and involves the following test statistic:
where 
is
the 
’th
order statistic, i.e. the ’th smallest value in the sample
and 
are
as follows, the 
are
the expected values of the order statistics of 
i.i.d. random
variables sampled from the standard Normal distribution and 
is
the covariance matrix of these order statistics:
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