The assumption of normality is required by several methods in parametricstatistical inference, some of which are robust toward mild or moderatenon-normality. The histogram in Fig. 1a was prepared with 20 values randomlygenerated with the standard normal distribution; however, one could arguethat the normality of the variable is not evident from the histogram. Ifthese were real observations instead of generated data, a test would beapplied with the null hypothesis being that the variable has a normaldistribution; frequently no specific distribution is mentioned as alternativehypothesis. The normal quantile plot (Fig. 1b) compares the ordered values\({x}_{(i)}\)in the sample, also calledorder statistics, with thencorresponding quantiles of the normal distribution. If the sample comes from anormal distribution, the dots tend to suggest a linear pattern. Other versions ofthe quantile plot do exist.
Numerous tests for normality have been defined. Tests are generally compared in terms of...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References and Further Reading
Bonett DG, Seier E (2002) A test of normality with high uniform power. Comput Stat Data An 40:435–445
Chen L, Shapiro S (1995) An alternative test for normality based on normalized spacings. J Stat Comput Sim 53:269–287
Coin DA (2008) Goodness-of-fit test for normality based on polynomial regression. Comput Stat Data An 52: 2185–2198
D’Agostino RB, Belanger A, D’Agostino RB Jr (1990) A suggestion for using powerful and informative tests of normality. Am Stat 44:316–322
Del Barrio E, Giné E, Utzet F (2005) Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances. Bernoulli 11: 131–189
Gan FF, Koehler KJ (1990) Goodness of fit tests based on P-P probability plots. Technometrics 32:289–303
Gel YR, Gastwirth JL (2008) A robust modification of the JarqueBera test of normality. Econ Lett 99:30–32
Gel YR, Miao W, Gastwirth JL (2007) Robust directed test of normality against heavy-tailed alternatives. Comput Stat Data An 51:2734–2746
Romão X, Delgado R, Costa A (2010) An empirical power comparison of univariate goodness-of-fit tests for normality. J Stat Comp Sim 80:545–591
Royston P (1989) Correcting the Shapiro–Wilk W for ties. J Stat Comput Sim 31:237–249
Royston P (1992) Approximating the Shapiro–Wilk W-test for non-normality. Stat Comput 2:117–119
Seier E (2002) Comparison of tests for univariate normality. Interstat, January 2002
Thode HC (2002) Testing for normality. Marcel Dekker, New York
Zhang J, Wu Y (2005) Likelihood-ratio tests for normality. Comput Stat Data An 49:709–721
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this entry
Cite this entry
Seier, E. (2011). Normality Tests: Power Comparison. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_421
Download citation
DOI: https://doi.org/10.1007/978-3-642-04898-2_421
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04897-5
Online ISBN: 978-3-642-04898-2
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering