Statistics and Computing

, Volume 2, Issue 3, pp 117-119

First online:

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

  • Patrick RoystonAffiliated withDepartment of Medical Physics, Royal Postgraduate Medical School

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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.


Non-normality Shapiro-WilkW-test