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

Abstract

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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Royston, P. Approximating the Shapiro-Wilk W-test for non-normality. Stat Comput 2, 117–119 (1992). https://doi.org/10.1007/BF01891203

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  • DOI: https://doi.org/10.1007/BF01891203

Keywords

  • Non-normality
  • Shapiro-WilkW-test