Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Comprehensive comparison of normality tests: Empirical study using many different types of data

  • Lee, Chanmi (Department of Statistics, Chonnam National University) ;
  • Park, Suhwi (Department of Statistics, Chonnam National University) ;
  • Jeong, Jaesik (Department of Statistics, Chonnam National University)
  • Received : 2016.07.04
  • Accepted : 2016.08.05
  • Published : 2016.09.30
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Abstract

We compare many normality tests consisting of different sources of information extracted from the given data: Anderson-Darling test, Kolmogorov-Smirnov test, Cramervon Mises test, Shapiro-Wilk test, Shaprio-Francia test, Lilliefors, Jarque-Bera test, D'Agostino' D, Doornik-Hansen test, Energy test and Martinzez-Iglewicz test. For the purpose of comparison, those tests are applied to the various types of data generated from skewed distribution, unsymmetric distribution, and distribution with different length of support. We then summarize comparison results in terms of two things: type I error control and power. The selection of the best test depends on the shape of the distribution of the data, implying that there is no test which is the most powerful for all distributions.

Keywords

References

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