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Recently I was trying to learn more about Normality tests and came to know about Shapiro-Wilk test for Normality. I understood most part of it but one thing I didn't understand is that how do I find the ai values to obtain the test statistic. As I don't know much about order statistics can anyone help me find the expected values and covariance matrix of the order statistics of independent and identically distributed random variables sampled from the standard normal distribution? Is there any formula to get those values? You can take any random sample to show it if you want. Thank you.

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    $\begingroup$ These require numerical calculation: that's why you cannot find formulas for the coefficients of the SW test statistics. $\endgroup$ – whuber Sep 1 at 14:28

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