Robustness to non-normality of common tests for the many-sample location problem

Journal of Applied Mathematics and Decision Sciences

Volumn 7, Issue 4, 2004, Pages 187-206

  Khan, Azmeri ^a   Rayner, Glen D ^b,c  

^a DEAKIN UNIVERSITY   (Australia)

^b NATIONAL AUSTRALIA BANK   (Australia)

^c UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

ANOVA; g and k distribution; Kruskal Wallis test; Quantile function

Indexed keywords

EID: 55449117031     PISSN: 11739126     EISSN: 15327612     Source Type: Journal    
DOI: 10.1155/S1173912603000178     Document Type: Article

References (18)

1. K. P. Balanda and H. L. MacGillivray. Kurtosis and spread. Canadian Journal of Statistics, 18:17-30, 1990.
2. K. R. Gabriel, and P. A. Lachenbruch. Non-parametric ANOVA in Small samples: A Monte Carlo study of the adequacy of the asymptotic approximation. Biometrics, Vol 25, 593-596, 1969.
3. M. A. Haynes, M. L. Gatton, and K. L. Mengersen. Generalized control charts for non-normal data. Technical Report Number 97/4, School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia, 1997a.
4. M. A. Haynes, H. L. MacGillivray, and K. L. Mengersen. Robustness of ranking and selection rules using generalized g-and-k distributions. Journal of Statistical Planning and Inference, 65:45-66, 1997b.
5. D. C. Hoaglin. Summarizing shape numerically: the g-and-h distributions. In D. C. Hoaglin, F. Mosteller, and J. W. Tukey (eds) Understanding Robust and Exploratory Data Analysis, Wiley, New York, 1985.
6. K. Ito. Robustness of ANOVA and MANOVA test procedures. In handbook of Statistics, Vol. 1, (P. R. Krishnainh, ed.), Amsterdam, Holand, 1980.
7. H. L. MacGillivray. Skewness and asymmetry: measures and orderings. The Annals of Statistics, 14:994-1011, 1986.
8. H. L. MacGillivray and K. P. Balanda. The relationships between skewness and kurtosis. Australian Journal of Statistics, 30:319-337, 1988.
9. H. L. MacGillivray. Shape properties of the g-and-h and Johnson families. Communications in Statistics - Theory and Methods, 21:1233-1250, 1992.
10. H. L. MacGillivray and W. H. Cannon. Generalizations of the g-and-h distributions and their uses. Preprint, 2002.
11. J. Martinez and B. Iglewicz. Some properties of the Tukey g-and-h family of distributions. Communications in Statistics - Theory and Methods, 13:353-369, 1984.
12. D. C. Montgomery. Design and Analysis of Experiments, 2nd ed. John Wiley, 1984.
13. J. S. Ramberg, P. R. Tadikamalla, E. J. Dudewicz, and E. F. Mykytka. A probability distribution and its uses in fitting data. Technometrics, 21:201-214, 1979.
14. G. D. Rayner. Statistical Methodologies for Quantile-based Distributional Families. PhD thesis, Queensland University of Technology, Australia, 2000.
15. G. D. Rayner and H. L. MacGillivray. Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions. Statistics & Computing, 12:57-75, 2002.
16. W. Y. Tan. Sampling distributions and robustness of t, f and variance-ratio in two samples and ANOVA Models with respect to departure from normality. Communications in Statistics - Theory and Methods, 11:2485-2511, 1982.
17. M. L. Tiku. Power function of the F-test under non-normal situations. Journal of the American Statistical Association, 66:913-915, 1971.
18. M. L. Tiku. Laguerre series forms of the distributions of classical test statistics and their robustness in non-normal situations. In Applied Statistics (R. P. Gupta, eds), New York, American Elsevier, 1975.