The Power to See: A New Graphical Test of Normality

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Statistics Papers
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confidence bands
graphical presentation
normality test
power analysis
quantile-quantile plot
Statistics and Probability
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Aldor-Noiman, Sivan
Brown, Lawrence D
Stine, Robert A
Buja, Andreas
Rolke, Wolfgang
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Abstract

Many statistical procedures assume the underlying data generating process involves Gaussian errors. Among the well-known procedures are ANOVA, multiple regression, linear discriminant analysis and many more. There are a few popular procedures that are commonly used to test for normality such as the Kolmogorov-Smirnov test and the ShapiroWilk test. Excluding the Kolmogorov-Smirnov testing procedure, these methods do not have a graphical representation. As such these testing methods offer very little insight as to how the observed process deviates from the normality assumption. In this paper we discuss a simple new graphical procedure which provides confidence bands for a normal quantile-quantile plot. These bands define a test of normality and are much narrower in the tails than those related to the Kolmogorov-Smirnov test. Correspondingly the new procedure has much greater power to detect deviations from normality in the tails.

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2013-01-01
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The American Statistician
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