Statistics Papers

Document Type

Journal Article

Date of this Version

2013

Publication Source

The American Statistician

Volume

67

Issue

4

Start Page

249

Last Page

260

DOI

10.1080/00031305.2013.847865

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.

Copyright/Permission Statement

This is an Accepted Manuscript of an article published by Taylor & Francis in The American Statistician on 11 Oct 2013, available online: http://wwww.tandfonline.com/10.1080/00031305.2013.847865.

Keywords

confidence bands, graphical presentation, normality test, power analysis, quantile-quantile plot

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Date Posted: 27 November 2017