Diagnostic limitations of skewness coefficients in assessing departures from univariate and multivariate normality

Ronald L. Horswell, Stephen Warwick Looney

Research output: Contribution to journalArticle

25 Scopus citations


While many tests of univariate and multivariate normality have been proposed, those based on skewness and kurtosis coefficients are widely presumed to offer the advantage of diagnosing how distributions depart from normality. However, results summarized from many Monte Carlo studies show that tests based on skewness coefficients do not reliably discriminate between skewed and non-skewed distributions. Indeed, the use of skewness tests to discriminate between these distributions lacks theoretical foundation. The performance of skewness tests is shown to be very sensitive to the kurtosis of the underlying distribution.

Original languageEnglish (US)
Pages (from-to)437-459
Number of pages23
JournalCommunications in Statistics - Simulation and Computation
Issue number2
Publication statusPublished - Jan 1 1993
Externally publishedYes



  • kurtosis
  • multivariate
  • normality
  • radii
  • skewness
  • univariate normality

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation

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