[Rd] bug in Shapiro Wilk Test

[Kurt Hornik]

>>>>> AK  writes:

Thanks.  What precisely is the problem you are seeing?

R uses Royston's

  ALGORITHM AS R94 APPL. STATIST. (1995) vol.44, no.4, 547-551

which in turn uses the improved approximations to the weights from 
<https://doi.org/10.1007/BF01891203>, and Table 1 in Hanusz et al would
seem to suggest that they are indeed accurate to two significant digits?

Best
-k


> 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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