Statistics and Computing

, Volume 2, Issue 3, pp 117–119

Approximating the Shapiro-Wilk W-test for non-normality


  • Patrick Royston
    • Department of Medical PhysicsRoyal Postgraduate Medical School

DOI: 10.1007/BF01891203

Cite this article as:
Royston, P. Stat Comput (1992) 2: 117. doi:10.1007/BF01891203


A new approximation for the coefficients required to calculate the Shapiro-WilkW-test is derived. It is easy to calculate and applies for any sample size greater than 3. A normalizing transformation for theW statistic is given, enabling itsP-value to be computed simply. The distribution of the new approximation toW agrees well with published critical points which use exact coefficients.


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© Chapman & Hall 1992