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

• Autorzy: Zofia Hanusz , Joanna Tarasińska
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Shapiro-Wilk W test; Kolmogorov-Smirnov test; normality; Johnson’s SB transformation

• Wydawca: De Gruyter Open
• Czasopismo: Biometrical Letters
• Rocznik: 2015
• Tom: 52
• Numer: 2
• Strony: 85-93

Daty

wydano

2015-12-01

online

2015-12-12

Twórcy

autor

Zofia Hanusz

• Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Głęboka 28, 20-612 Lublin, Poland

autor

Joanna Tarasińska

• Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Głęboka 28, 20-612 Lublin, Poland

Bibliografia

• 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]
• Johnson N.L. (1949): Systems of frequency curves generated by methods of translation. Biometrika 36: 149-176.[Crossref]
• Hanusz Z., Tarasińska J. (2014): Normalization of Shapiro-Wilk test with known mean. Colloquium Biometricum 44: 35-41.
• Kolmogorov A. (1933): Sulla derminazione empirica di una legge di distribuzione. Ist. Ital. Attuari G,4: 1-11.
• Marsaglia G., Tsang W.W., Wang J. (2003): Evaluating Kolmogorov’s distribution. Journal of Statistical Software 8/18.
• Miller L.H. (1956): Table of percentage points of Kolmogorov statistics. J. Amer. Statist. Assoc. 51: 111-121.[Crossref]
• 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.
• Rao C.R. (1948): Tests of significance in multivariate analysis. Biometrika 35: 58-79.[Crossref]
• Royston J.P. (1992): Approximating the Shapiro-Wilk W-test for non-normality. Statistics and Computing 2: 117-119.[Crossref]
• Shapiro S.S., Wilk M.B. (1965): An analysis of variance test for normality (complete samples). Biometrika 52: 591-611.[Crossref]
• Shapiro S.S., Wilk M.B. (1968): Approximations for the null distribution of the W statistic. Technometrics 10: 861-866.[Crossref]
• Stephens M.A. (1974): EDF statistics for goodness of fit and some comparisons. JASA, 69(347): 730-737.
• Thode H.C. (2002): Testing for normality. Marcel Dekker Inc.

Identyfikatory

DOI

10.1515/bile-2015-0008