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The Power to See: A New Graphical Test of Normality

Author

Listed:
  • Sivan Aldor-Noiman
  • Lawrence D. Brown
  • Andreas Buja
  • Wolfgang Rolke
  • Robert A. Stine

Abstract

Many statistical procedures assume that the underlying data-generating process involves Gaussian errors. Among the popular tests for normality, only the Kolmogorov--Smirnov test has a graphical representation. Alternative tests, such as the Shapiro--Wilk test, offer little insight as to how the observed data deviate from normality. In this article, we discuss a simple new graphical procedure which provides simultaneous confidence bands for a normal quantile--quantile plot. These bands define a test of normality and are narrower in the tails than those related to the Kolmogorov--Smirnov test. Correspondingly, the new procedure has greater power to detect deviations from normality in the tails. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:amstat:v:67:y:2013:i:4:p:249-260
    DOI: 10.1080/00031305.2013.847865
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    Cited by:

    1. Robert Arscott, 2023. "Market Efficiency and Censoring Bias in College Football Gambling," Journal of Sports Economics, , vol. 24(5), pages 664-689, June.
    2. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    3. 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.
    4. Surya T. Tokdar & Ryan Martin, 2021. "Bayesian Test of Normality Versus a Dirichlet Process Mixture Alternative," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 66-96, May.
    5. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    6. Robert A. Stine, 2017. "Explaining Normal Quantile-Quantile Plots Through Animation: The Water-Filling Analogy," The American Statistician, Taylor & Francis Journals, vol. 71(2), pages 145-147, April.
    7. Marc S. Paolella, 2015. "New Graphical Methods and Test Statistics for Testing Composite Normality," Econometrics, MDPI, vol. 3(3), pages 1-29, July.

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