Good Text for Shapiro-Wilk Test I was wondering if anyone can give me some good texts for understanding the Shapiro-Wilk test.
I'm searching for an intermediate level text, not too simple like the wikipedia page (it gives very little information) and not too complicated like the original paper from the two authors.
Any suggestion is appreciated! 
Thank you guys !!
 A: You may find the discussion of the test in D'Agostino & Stephens' Goodness of Fit Techniques of some use. 
It is a ratio of two different estimates of variance under normality, the denominator the usual variance estimate and the numerator one based on the square of a linear function of the order statistics.
Apart from a scaling factor in the numerator and denominator, you can see that at the Wikipedia page for the test
It's also closely related to a linear function of the squared correlation between the order statistics (the values sorted into order) and the expected normal order statistics (i.e. it's closely related to the Shapiro-Francia and Ryan-Joiner tests) -- e.g. see the first page here https://www1.fpl.fs.fed.us/spl1991.pdf, the paragraph starting "Filliben", but uses information in the covariance of the order statistics to get a (usually) somewhat more powerful test for small samples.
There's also a large number of questions on site about the Shapiro-Wilk test (I've answered more than 50, so there'll be considerably more than that) at least some of which address the things you are after, so I'd also recommend trying a site-search.
