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Visualizing Type II Error in Normality Tests

Author

Listed:
  • José A. Sánchez-Espigares
  • Pere Grima
  • Lluís Marco-Almagro

Abstract

A skewed exponential power distribution, with parameters defining kurtosis and skewness, is introduced as a way to visualize Type II error in normality tests. By varying these parameters a mosaic of distributions is built, ranging from double exponential to uniform or from positive to negative exponential; the normal distribution is a particular case located in the center of the mosaic. Using a sequential color scheme, a different color is assigned to each distribution in the mosaic depending on the probability of committing a Type II error. This graph gives a visual representation of the power of the performed test. This way of representing results facilitates the comparison of the power of various tests and the influence of sample size. A script to perform this graphical representation, programmed in the R statistical software, is available online as supplementary material.

Suggested Citation

  • José A. Sánchez-Espigares & Pere Grima & Lluís Marco-Almagro, 2018. "Visualizing Type II Error in Normality Tests," The American Statistician, Taylor & Francis Journals, vol. 72(2), pages 158-162, April.
    • Handle: RePEc:taf:amstat:v:72:y:2018:i:2:p:158-162
    DOI: 10.1080/00031305.2016.1278035
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    References listed on IDEAS

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    1. Zhu, Dongming & Zinde-Walsh, Victoria, 2009. "Properties and estimation of asymmetric exponential power distribution," Journal of Econometrics, Elsevier, vol. 148(1), pages 86-99, January.
    2. Sivan Aldor-Noiman & Lawrence D. Brown & Andreas Buja & Wolfgang Rolke & Robert A. Stine, 2013. "The Power to See: A New Graphical Test of Normality," The American Statistician, Taylor & Francis Journals, vol. 67(4), pages 249-260, November.
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