Someone may want to read the paper more closely, but as far as I can tell, they compare their variant to the original S-W test, then say almost in passing that their constants are similar to those of Royston (1992). R implements AS R94, which is by Royston:
A Remark on Algorithm AS 181: The W-Test for Normality Purchased Patrick Royston Journal of the Royal Statistical Society Series C: Applied Statistics, Volume 44, Issue 4, December 1995, Pages 547–551, https://doi.org/10.2307/2986146 > On 22 May 2026, at 10.26, AK <[email protected]> wrote: > > 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 > > Abstract > > The 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] > --------------------------------------------------- > > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: [email protected] Priv: [email protected] ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
