Good afternoon,This concerns the Shapiro-Wilk test for normal distribution in the field of mathematical statistics. Did you take into account the latest research findings from the 2014 publication by Hanusz & Tarasińska (1) when calculating the coefficients for the W-statistic? Both authors point out an error in the original work by Shapiro and Wilk.
If you have not yet corrected the coefficient calculation, this could lead to incorrect decisions in the case of the so-called H0 hypothesis.
I hope you find this helpful. Best regards Alexander Kud(1) Zofia Hanusz & Joanna TarasiŃska (2014) Simulation Study on Improved Shapiro–Wilk Tests for Normality, Communications in Statistics - Simulation and Computation, 43:9, 2093-2105, DOI: 10.1080/03610918.2013.844835
Link to this article: http://dx.doi.org/10.1080/03610918.2013.844835 AbstractThe article concerns tests for normality based on the Shapiro–Wilk W statistic. The constants in the test statistic are recalculated as those given in Shapiro and Wilk are incorrect. The empirical significance levels and power of improved tests have been evaluated in simulation study and compared to original ones. The improved tests were also applied to the multivariate case. In this case, we consider two implementations of the W statistic, the first one proposed by Srivastava and Hui and the other by Hanusz and Tarasinska. Empirical size of tests and their power have been compared to the Henze–Zirkler test.
--------------------------------------------------- Dr. Alexander Kud Scientist in Physical Chemistry [email protected] ---------------------------------------------------
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