Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

Zofia Hanusz; Joanna Tarasińska

Biometrical Letters (2015)

  • Volume: 52, Issue: 2, page 85-93
  • ISSN: 1896-3811

Abstract

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Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.

How to cite

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Zofia Hanusz, and Joanna Tarasińska. "Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality." Biometrical Letters 52.2 (2015): 85-93. <http://eudml.org/doc/276014>.

@article{ZofiaHanusz2015,
abstract = {Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.},
author = {Zofia Hanusz, Joanna Tarasińska},
journal = {Biometrical Letters},
keywords = {Shapiro-Wilk W test; Kolmogorov-Smirnov test; normality; Johnson’s SB transformation; empirical significance level; Henze-Zirkler test; power; Srivastava-Hui test; testing normality},
language = {eng},
number = {2},
pages = {85-93},
title = {Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality},
url = {http://eudml.org/doc/276014},
volume = {52},
year = {2015},
}

TY - JOUR
AU - Zofia Hanusz
AU - Joanna Tarasińska
TI - Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality
JO - Biometrical Letters
PY - 2015
VL - 52
IS - 2
SP - 85
EP - 93
AB - Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.
LA - eng
KW - Shapiro-Wilk W test; Kolmogorov-Smirnov test; normality; Johnson’s SB transformation; empirical significance level; Henze-Zirkler test; power; Srivastava-Hui test; testing normality
UR - http://eudml.org/doc/276014
ER -

References

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  1. Birnbaum Z.W. (1952): Numerical tabulation of the distribution of Kolmogorov’s statistic for finite sample size. J. Amer. Statist. Assoc. 47: 425-44.[Crossref] Zbl0047.38103
  2. Johnson N.L. (1949): Systems of frequency curves generated by methods of translation. Biometrika 36: 149-176.[Crossref] Zbl0033.07204
  3. Hanusz Z., Tarasińska J. (2014): Normalization of Shapiro-Wilk test with known mean. Colloquium Biometricum 44: 35-41. Zbl06330996
  4. Kolmogorov A. (1933): Sulla derminazione empirica di una legge di distribuzione. Ist. Ital. Attuari G,4: 1-11. 
  5. Marsaglia G., Tsang W.W., Wang J. (2003): Evaluating Kolmogorov’s distribution. Journal of Statistical Software 8/18. 
  6. Miller L.H. (1956): Table of percentage points of Kolmogorov statistics. J. Amer. Statist. Assoc. 51: 111-121.[Crossref] Zbl0071.13301
  7. R Development Core Team (2008): R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org. 
  8. Rao C.R. (1948): Tests of significance in multivariate analysis. Biometrika 35: 58-79.[Crossref] Zbl0031.06202
  9. Royston J.P. (1992): Approximating the Shapiro-Wilk W-test for non-normality. Statistics and Computing 2: 117-119.[Crossref] 
  10. Shapiro S.S., Wilk M.B. (1965): An analysis of variance test for normality (complete samples). Biometrika 52: 591-611.[Crossref] Zbl0134.36501
  11. Shapiro S.S., Wilk M.B. (1968): Approximations for the null distribution of the W statistic. Technometrics 10: 861-866.[Crossref] 
  12. Stephens M.A. (1974): EDF statistics for goodness of fit and some comparisons. JASA, 69(347): 730-737. 
  13. Thode H.C. (2002): Testing for normality. Marcel Dekker Inc. Zbl1032.62040

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