Testing experimental data for univariate normality

Clinica Chimica Acta

Volumn 366, Issue 1-2, 2006, Pages 112-129

  Henderson, A Ralph ^a,b  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

^b NONE   (Canada)

Author keywords

Graphical techniques; Kurtosis; L moments; Royston's v test; Skewness; Tests for normality

Indexed keywords

ANALYTIC METHOD; ARTICLE; CLINICAL CHEMISTRY; CORRELATION ANALYSIS; HISTOGRAM; NORMAL DISTRIBUTION; PRIORITY JOURNAL; PROBABILITY; REGRESSION ANALYSIS; SAMPLE SIZE; STATISTICAL ANALYSIS;

EID: 33644682134     PISSN: 00098981     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cca.2005.11.007     Document Type: Review

References (74)

1. K. Linnet Testing normality of transformed data Appl Stat 37 1988 180 186
2. P. Horn, and A.J. Pesce Reference intervals. A user's guide 2005 AACC Press Washington, DC 1 123
3. H.E. Solberg Chapter 16: establishment and use of reference values C.A. Burtis E.R. Ashwood D.E. Bruns Tietz textbook of clinical chemistry and molecular diagnostics 4th ed. 2005 Elsevier Saunders St. Louis 425 448
4. E.M. Wright, and P. Royston Calculating reference intervals for laboratory measurements Stat Methods Med Res 8 1999 93 112
5. H.E. Solberg RefVal: a program implementing the recommendations of the International Federation of Clinical Chemistry on the statistical treatment of reference values Comput Methods Programs Biomed 48 1995 247 256
6. R.B. D'Agostino M.A. Stephens Goodness-of-fit techniques 1986 Marcel Dekker, Inc. New York 1 560
7. H.C.J. Thode Testing for normality 2002 Marcel Dekker, Inc. New York 1 479
8. F.Y. Leung, L.V. Galbraith, G. Jablonsky, and A.R. Henderson Re-evaluation of the diagnostic utility of serum total creatine kinase and creatine kinase-2 in myocardial infarction Clin Chem 35 1989 1435 1440
9. R Development Core Team. R: A language and environment for statistical computing. http://www.R-project.org. (Accessed 19-10-2005).
10. J. Fox An R and S-PLUS companion to applied regression 2002 Sage Publications, Inc. Thousand Oaks, CA 1 312
11. J.W. Tukey Exploratory data analysis 1977 Addison-Wesley Publishing Company Reading, MA 1 688
12. E.S. Pearson, and N.W. Please Relation between the shape of population distribution and the robustness of four simple test statistics Biometrika 62 1975 223 241
13. H. Cramér Mathematical methods of statistics 1946 Princeton University Press Princeton 1 575
14. A. Stuart, and J.K. Ord Kendall's advanced theory of statistics Distribution theory, volume 1 6th ed. 1994 Arnold London 1 676
15. E.A. Cornish, and R.A. Fisher Moments and cumulants in the specification of distributions Rev Int Stat Inst 5 1937 307 322
16. D.N. Joanes, and C.A. Gill Comparing measures of sample skewness and kurtosis Statistician 47 1998 183 189
17. A. Stuart, J.K. Ord, and S. Arnold Kendall's advanced theory of statistics Classical inference and the linear model, volume 2A 6th ed. 1999 Arnold London 1 885
18. R.B. D'Agostino Chapter 9: tests for the normal distribution Goodness-of-fit techniques 1986 Marcel Dekker, Inc. New York 367 419
19. 2 Biometrika 57 1970 679 681
20. F.J. Anscombe, and W.J. Glynn Distribution of the kurtosis statistic b2 for normal samples Biometrika 70 1983 227 234
21. A. Hald Statistical theory with engineering applications 1952 John Wiley and Sons, Inc. New York 1 783
22. R.B. D'Agostino, A. Belanger, and R.B. D'Agostino Jr. A suggestion for using powerful and informative tests of normality Am Stat 44 1990 316 321
23. W. Kirby Algebraic boundedness of sample statistics Water Resour Res 10 1974 220 222
24. J. Dalén Algebraic bounds on standardized sample moments Stat Probab Lett 5 1987 329 331
25. M.E. Johnson, and V.W. Lowe Bounds on the sample skewness and kurtosis Technometrics 21 1979 377 378
26. K.P. Balanda, and H.L. MacGillivray Kurtosis: a critical review Am Stat 42 1988 111 119
27. J.R.M. Hosking L-moments: analysis and estimation of distributions using linear combinations of order statistics JR Stat Soc B 52 1990 105 124
28. J.A. Greenwood, J.M. Landwehr, N.C. Matalas, and J.R. Wallis Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form Water Resour Res 15 1979 1049 1054
29. P. Royston Which measures of skewness and kurtosis are best? Stat Med 11 1992 333 343
30. J.R.M. Hosking, and J.R. Wallis Regional frequency analysis. An approach based on L-moments 1997 Cambridge University Press Cambridge 1 224
31. Q.J. Wang Direct sample estimators of L-moments Water Resour Res 32 1996 3617 3619
32. J.R.M. Hosking Moments or L-moments? An example comparing two measures of distributional shape Am Stat 46 1992 186 189
33. B. Efron, and R. Tibshirani An introduction to the bootstrap 1993 Chapman and Hall New York 1 436
34. E.A.H. Elamir, and A.H. Seheult Trimmed L-moments Comp Stat Data Anal 43 2003 299 314
35. R.M. Vogel, and N.M. Fennessey L-moment diagrams should replace product moment diagrams Water Resour Res 29 1993 1745 1752
36. Hosking JRM. Fortran routines for use with the method of L-moments. http://lib.stat.cmu.edu/general/lmoments. (Accessed 19-4-2005).
37. Hosking JRM. SAMLMU: estimating sample L-moments. http://www.r-project. org/nocvs/mail/r-help/2001/6042.html. (Accessed 20-11-2005).
38. R.C. Geary The ratio of the mean deviation to the standard deviation as a test for normality Biometrika 27 1935 310 332
39. R.C. Geary Moments of the ratio of the mean deviation to the standard deviation for normal samples Biometrika 28 1936 295 305
40. R.B. D'Agostino, and B. Rosman The power of Geary's test of normality Biometrika 61 1974 181 184
41. R.B. D'Agostino Simple compact portable test of normality: Geary's test revisited Psychol Bull 74 1970 138 140
42. G. van Belle, L.D. Fisher, P.J. Heagerty, and T. Lumley Biostatistics: a methodology for the health sciences 2nd ed. 2004 Wiley Interscience New York 1 871
43. D.S. Moore Chapter 3: tests of chi-squared type R.B. D'Agostino M.A. Stephens Goodness-of-fit techniques 1986 Marcel Dekker, Inc. New York 63 95
44. M.A. Stephens Chapter 4: tests based on EDF statistics R.B. D'Agostino M.A. Stephens Goodness-of-fit techniques 1986 Marcel Dekker, Inc. New York 97 193
45. W.J. Conover Chapter 6: statistics of the Kolmogorov-Smirnov type Practical nonparametric statistics 2nd ed. 1980 John Wiley and Sons New York 344 393
46. M.A. Stephens EDF statistics for goodness of fit and some comparisons J Am Stat Assoc 69 1974 730 737
47. F.J. Massey The Kolmogorov-Smirnov test for goodness-of-fit J Am Stat Assoc 46 1951 68 78
48. H.W. Lilliefors On the Kolmogorov-Smirnov test for normality with mean and variance unknown J Am Stat Assoc 62 1967 399 402
49. A.L. Mason, and C.B. Bell New Lilliefors and Srinivasan tables with applications Comm Stat-Simul 15 1986 451 467
50. G.E. Dallal, and L. Wilkinson An analytic approximation to the distribution of Lilliefor's test statistic for normality Am Stat 40 1986 294 296
51. R.L. Iman Graphs for use with the Lilliefors test for normal and exponential distributions Am Stat 36 1982 109 112
52. T.W. Anderson, and D.A. Darling Asymptotic theory of certain "goodness of fit" criteria based on stochastic processes Ann Math Stat 23 1952 193 212
53. T.W. Anderson, and D.A. Darling A test of goodness of fit J Am Stat Assoc 49 1954 765 769
54. M.A. Stephens Chapter 5: tests based on regression and correlation R.B. D'Agostino M.A. Stephens Goodness-of-fit techniques 1986 Marcel Dekker, Inc. New York 195 233
55. F.F. Gan, and K.J. Koehler Goodness-of-fit tests based on P-P probability plots Technometrics 32 1990 289 303
56. S.S. Shapiro, and M.B. Wilk An analysis of variance test for normality (complete samples) Biometrika 52 1965 591 611
57. S.S. Shapiro, and M.B. Wilk Approximations for the null distribution of the W statistic Technometrics 10 1968 861 866
58. J.P. Royston An extension of Shapiro and Wilk's W test for normality to large samples Appl Stat 31 1982 115 124
59. J.P. Royston Approximating the Shapiro-Wilk W-test for non-normality Stat Comput 2 1982 117 119
60. P. Royston A remark on algorithm AS 181: the W-test for normality Appl Stat 44 1995 547 551
61. E.S. Pearson, and H.O. Hartley Biometrika tables for statisticians, volume two, reprinted with corrections 1976 Biometrika Trust London 1 385
62. J.P. Royston Algorithm AS 181: the W test for normality Appl Stat 31 1982 176 180
63. S.S. Shapiro, and R.S. Francia An approximate analysis of variance test for normality J Am Stat Assoc 67 1972 215 216
64. P. Royston A toolkit for testing for non-normality in complete and censored samples Statistician 42 1993 37 43
65. P. Royston A pocket-calculator algorithm for the Shapiro-Francia test for non-normality: an application to medicine Stat Med 12 1993 181 184
66. J.J. Filliben The probability plot correlation coefficient test for normality Technometrics 17 1975 111 117
67. P. Royston Estimating departure from normality Stat Med 10 1991 1283 1293
68. S.S. Shapiro, M.B. Wilk, and H.J. Chen A comparative study of various tests for normality J Am Stat Assoc 63 1968 1343 1372
69. E.H. Chen The power of the Shapiro-Wilk W test for normality in samples from contaminated normal distributions J Am Stat Assoc 66 1971 760 762
70. E.S. Pearson, R.B. D'Agostino, and K.O. Bowman Tests for departure from normality: comparison of powers Biometrika 64 1977 231 246
71. K. Pearson On a criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen in random sampling Phil Mag 50 1900 157 175
72. H. Cramér On the composition of elementary errors. II: statistical applications Skand Aktuartidskr 11 1928 141 180
73. von Mises, R. Wahrscheinlichkeitsrechnung. Leipzig-Wein 1931.
74. 2 C R Acad Sci Paris 202 1936 449 452