[Rd] bug in Shapiro Wilk Test

[peter dalgaard]

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 <alexander.e.kud using yandex.com> 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
> 
> alexander.e.kud using yandex.com
> ---------------------------------------------------
> 
> 
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-- 
Peter Dalgaard, Professor,
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