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Explaining Normal Quantile-Quantile Plots Through Animation: The Water-Filling Analogy

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  • Robert A. Stine

Abstract

A normal quantile-quantile (QQ) plot is an important diagnostic for checking the assumption of normality. Though useful, these plots confuse students in my introductory statistics classes. A water-filling analogy, however, intuitively conveys the underlying concept. This analogy characterizes a QQ plot as a parametric plot of the water levels in two gradually filling vases. Each vase takes its shape from a probability distribution or sample. If the vases share a common shape, then the water levels match throughout the filling, and the QQ plot traces a diagonal line. An R package qqvases provides an interactive animation of this process and is suitable for classroom use.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:amstat:v:71:y:2017:i:2:p:145-147
    DOI: 10.1080/00031305.2016.1200488
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    References listed on IDEAS

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    1. George Cobb, 2015. "Mere Renovation is Too Little Too Late: We Need to Rethink our Undergraduate Curriculum from the Ground Up," The American Statistician, Taylor & Francis Journals, vol. 69(4), pages 266-282, November.
    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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