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Original Articles

Comparisons of various types of normality tests

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Pages 2141-2155 | Received 03 Jun 2010, Accepted 29 Aug 2010, Published online: 18 May 2011

References

  • D'Agostino , R. B. and Stephens , M. A. 1986 . Goodness-of-fit Techniques , NewYork : Marcel Dekker .
  • Shapiro , S. S. , Wilk , M. B. and Chen , H. J. 1968 . A comparative study of various test for normality . J. Amer. Statist. Assoc. , 63 ( 324 ) : 1343 – 1372 .
  • Pearson , E. S. , D'Agostino , R. B. and Bowman , K. O. 1977 . Test for departure from normality: Comparison of powers . Biometrika , 64 ( 2 ) : 231 – 246 .
  • Wong , W. K. and Sim , C. H. 2000 . Goodness-of-fit based on empirical characteristic function . J. Statist. Comput. Simul. , 65 : 243 – 269 .
  • Keskin , S. 2006 . Comparison of several univariate normality tests regarding Type I error rate and power of the test in simulation based on small samples . J. Appl. Sci. Res. , 2 ( 5 ) : 296 – 300 .
  • Oztuna , D. , Elhan , A. H. and Tuccar , E. 2006 . Investigation of four different normality tests in terms of Type I error rate and power under different distributions . Turk. J. Med. Sci. , 36 ( 3 ) : 171 – 176 .
  • Farrell , P. J. and Rogers-Stewart , K. 2006 . Comprehensive study of tests for normality and symmetry: Extending the Spiegelhalter test . J. Statist. Comput. Simul. , 76 ( 9 ) : 803 – 816 .
  • Thadewald , T. and Buning , H. 2007 . Jarque–Bera test and its competitors for testing normality – a power comparison . J. Appl. Statist. , 34 ( 1 ) : 87 – 105 .
  • Yazici , B. and Yolacan , S. 2007 . A comparison of various tests of normality . J. Statist. Comput. Simul. , 77 ( 2 ) : 175 – 183 .
  • Shapiro , S. S. and Wilk , M. B. 1965 . An analysis of variance test for normality(complete samples) . Biometrika , 52 : 591 – 611 .
  • Royston , J. P. 1995 . Remark AS R94: A remark on Algorithm AS 181: The W-test for normality . Appl. Statist. , 44 : 547 – 551 .
  • Dallal , G. E. and Wilkinson , L. 1986 . An analytic approximation to the distribution of the Lilliefor's test statistic for normality . Amer. Statist. , 40 : 294 – 296 .
  • D'Agostino , R. B. , Belanger , A. and D'Agostino , R. B. Jr . 1990 . A suggestion for using powerful and informative tests of normality . Amer. Statist. , 44 ( 4 ) : 316 – 321 .
  • D'Agostino , R. B. and Pearson , E. S. 1973 . Testing for departures from normality. I. Fuller empirical results for the distribution of b2 and √b1 . Biometrika , 60 : 613 – 622 .
  • Royston , J. P. 1982 . An extension of Shapiro and Wilk's W test for normality to large samples . Appl. Statist. , 31 : 115 – 124 .
  • Royston , J. P. 1982 . The W test for normality . Appl. Stat. , 31 : 176 – 180 .
  • Royston , J. P. 1982 . Expected normal order statistics (exact and approximate), Appl. Statist. . 31 : 161 – 165 .
  • Royston , J. P. 1992 . Approximating the Shapiro–Wilk W test for non-normality . Stat. Comput. , 2 : 117 – 119 .
  • Shapiro , S. S. and Francia , R. S. 1972 . An approximate analysis of variance test for normality . J. Amer. Statist. Assoc. , 67 ( 337 ) : 215 – 216 .
  • Weisberg , S. and Bingham , C. 1975 . An approximate analysis of variance test for non-normality suitable for machine computation . Technometrics , 17 : 133 – 134 .
  • Rahman , M. M. and Govindarajulu , Z. 1997 . A modification of the test of Shapiro and Wilk for normality . J. Appl. Statist. , 14 ( 2 ) : 219 – 235 .
  • Kolmogorov , A. N. 1933 . Sulla determinazione empirica di una legge di distribuzione . Giornale dell’ Instituto Italiano degli Attuari 4 , : 83 – 91 .
  • Cramer , H. 1928 . On the composition of elementary errors . Skandinavisk Aktuarietidskrift , 11 : 13 – 74 . 141–180
  • Anderson , T. W. and Darling , D. A. 1954 . A test of goodness of fit . J. Amer. Statist. Assoc. , 49 ( 268 ) : 765 – 769 .
  • Lilliefors , H. W. 1967 . On the Kolmogorov–Smirnov test for normality with mean and variance unknown . J. Amer. Statist. Assoc. , 62 : 534 – 544 .
  • Lilliefors , H. W. 1969 . On the Kolmogorov–Smirnov test for the exponential distribution with mean unknown . J. Amer. Statist. Assoc. , 64 : 387 – 389 .
  • Conover , W. J. 1999 . Practical Nonparametric Statistics , 3 , New York : John Wiley and Sons .
  • von Mises , R. 1931 . Wahrscheinlichkeitsrechnung und Ihre Anwendung in der Statistik und Theoretischen Physik Edited by: Deuticke , F. Vol. 6.1 , Leipzig
  • N.V. Smirnov, Sui la distribution de w2 (Criterium de M.R.v. Mises), C.R. (Paris) 202(1936), pp. 449–452 (6.1)
  • A.W. Marshall, The small sample distribution of , Ann. Math. Statist. 29(1958) pp. 307–309
  • M.A. Stephens and U.R. Maag, Further percentage points for . Biometrika 55(2) (1968) pp. 428–430
  • Pearson , K. 1900 . On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can reasonably be supposed to have arisen from random sampling . Philos. Mag. , 50 ( 5 ) : 157 – 175 .
  • Schorr , B. 1974 . On the choice of the class intervals in the application of chi-square test . Oper. Forsch. U. Stat. , 5 : 357 – 377 .
  • Jarque , C. M. and Bera , A. K. 1987 . A test for normality of observations and regression residuals . Int. Stat. Rev. , 55 ( 2 ) : 163 – 172 .
  • Bowman , K. O. and Shenton , L. R. 1975 . Omnibus test contours for departures from normality based on √b1 and b2 . Biometrika , 62 ( 2 ) : 243 – 250 .
  • Ramberg , J. S. and Schmeiser , B. W. 1974 . An approximate method for generating asymmetric random variables . Commun. ACM , 17 : 78 – 82 .
  • Hastings , C. , Mosteller , F. , Tukey , J. W. and Winsor , C. P. 1947 . Low moments for small samples: A comparative study of statistics . Ann. Math. Statist. , 18 : 113 – 136 .
  • Karian , Z. A. and Dudewicz , E. J. 2000 . Fitting Statistical Distributions: The Generalized Lambda Distribution and the Generalized Bootstrap Methods , New York : CRC Press .
  • Rao , J. S. 1976 . Some tests based on arc-lengths for the circle . Sankhya B(4) , 38 : 329 – 338 .
  • Rao , J. S. and Kuo , M. 1984 . Asymptotic results on the Greenwood statistic and some of its generalizations . J. R. Statist. Soc. Ser. B , 46 : 228 – 237 .

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