Non-normally distributed data and non-parametric statistics

Richard A. Armstrong

Research output: Contribution to journalArticle


Different types of numerical data can be collected in a scientific investigation and the choice of statistical analysis will often depend on the distribution of the data. A basic distinction between variables is whether they are ‘parametric’ or ‘non-parametric’. When a variable is parametric, the data come from a symmetrically shaped distribution known as the ‘Gaussian’ or ‘normal distribution’ whereas non-parametric variables may have a distribution which deviates markedly in shape from normal. This article describes several aspects of the problem of non-normality including: (1) how to test for two common types of deviation from a normal distribution, viz., ‘skew’ and ‘kurtosis’, (2) how to fit the normal distribution to a sample of data, (3) the transformation of non-normally distributed data and scores, and (4) commonly used ‘non-parametric’ statistics which can be used in a variety of circumstances.
Original languageEnglish
Pages (from-to)26
Number of pages1
JournalOptometry Today
Issue number16
Publication statusPublished - 19 Aug 2011


  • numerical data
  • scientific investigation
  • choice
  • statistical analysis
  • distribution of data
  • parametric
  • distribution


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