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General Notes
Per Fundamental Concepts in the Design of Experiments (Hicks), "the Shapiro-Wilk test is one of the most powerful tests of normality when the sample size is less than 50."

From NIST - Shapiro-Wilk:
"The Shapiro-Wilk test, proposed in 1965, calculates a W statistic that tests whether a random sample, x1, x2, ..., xn comes from (specifically) a normal distribution . Small values of W are evidence of departure from normality and percentage points for the W statistic, obtained via Monte Carlo simulations, were reproduced by Pearson and Hartley (1972, Table 16). This test has done very well in comparison studies with other goodness of fit tests."





NIST - Shapiro-Wilk test description

Wikipedia - Shapiro-Wilk

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.