Statistics and Computing

, Volume 2, Issue 3, pp 117–119

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

  • Patrick Royston

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.



Copyright information

© Chapman & Hall 1992

Authors and Affiliations

  • Patrick Royston
    • 1
  1. 1.Department of Medical PhysicsRoyal Postgraduate Medical SchoolLondon