Selection of One-Stage Sample Size in Chen-Chen-Chang's tilde R Test and an Evaluation of the Performance of tilde R  ABSTRACT  |  FULL TEXT  Hacettepe Journal of Mathematics and Statistics

Year 2010, Volume: 39 Issue: 4, 613 - 626, 01.04.2010

B. Altunkaynak  h. Gamgam

https://izlik.org/JA52DD97NH

Keywords

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References

• Archambault, W. A. T., Mack, G. A. and Wolfe, D. A. K-sample rank tests using pair-specific scoring functions, Canad. J. Statist. 5, 195–207, 1977.
• Bartholomew, D. J. Ordered tests in the analysis of variance, Biometrika 48, 325–332, 1961. [3] Bishop, T. A. Heteroscedastic ANOVA, MANOVA and multiple comparisons (Unpublished Ph.D. Thesis, The Ohio State University, Ohio, 1976).
• Bishop, T. A. and Dudewicz, E. J. Exact analysis of variance with unequal variances: Test procedures and tables, Technometrics 20, 419–430, 1978.
• Bishop, T. A. and Dudewicz, E. J. Heteroscedastic ANOVA, Sankhya 43(B), 40–57, 1981. [6] Bucchianico, A. D. Computer algebra, combinatorics, and the Wilcoxon-Mann-Whitney statistic, J. Stat. Plan. Inf. 79, 349–364, 1999.
• Chacko, V. J. Testing homogeneity against ordered alternatives, Ann. Math. Statist. 34, 945–956, 1963.
• Chen, S. One-stage and two-stage statistical inference under heteroscedasticity, Communi- cations in Statistics: Simulation and Computation 30 (4), 991–1009, 2001.
• Chen, S. and Chen, J. H. Single-stage analysis of variance under heteroscedasticity, Com- munications Comm. Statist. Simulation 27 (3), 641–666, 1998.
• Chen, S., Chen, J. H., and Chang, H. F. A one-stage procedure for testing homogeneity of means against an ordered alternative under unequal variances, Communications in Statis- tics: Simulation and Computation 33 (1), 49–67, 2004.
• Daniel, W. W. Applied nonparametric statistics (Houghton Mifflin, Boston, 1978).
• Gamage, J., Mathew, T., and Weerahandi, S. Generalized p-values and generalized confi- dence regions for the multivariate Behrens-Fisher problem and MANOVA, J. Multivariate Anal. 88, 177–189, 2004.
• Gerami, A. and Zahedian, A. Comparing the means of normal populations with unequal variances(Proceedings of the 53rd Session of International Statistical Institute, Seoul, Korea 2001).
• Gibbons, J. D. Nonparametric Statistical Inference (McGraw-Hill Book Company, New York, 1971).
• Hettmansperger. T. P. and Norton, R. M. Tests for patterned alternatives in k-sample prob- lems, Journal of the American Statistical Association 82, 292–299, 1987.
• Jonckheere, A. R. A distribution-free k-sample test against ordered alternatives, Biometrika 41, 133–145, 1954.
• Lee, S. and Ahn, C. H. Modified ANOVA for unequal variances, Communications in Statis- tics: Simulation and Computation 32, 987–1004, 2003.
• Odeh, R. E. On Jonckheere’s k-sample test against ordered alternatives, Technometrics 13, 912–918, 1971.
• Puri, M. L. Some distribution-free k-sample rank tests of homogeneity against ordered al- ternatives, Comm. Pure Appl. Math. 18, 51–63. 1965.
• Rice, W. R. and Gaines, S. D. One-way analysis of variance with unequal variances, Proc. Nat. Acad. Sci. 86, 8183–8184, 1989.
• Terpstra, T. J. The asymptotic normality and consistency of Kendall’s test against trend, when ties are present in one ranking, Indigationes Mathematicae 14, 327–333, 1952.
• Weerahandi, S. ANOVA under unequal error variances, Biometrics 51, 589–599, 1995.
• Wiel, M. A. Exact distributions of distribution-free test statistics (Ph.D. Thesis, Eindhoven University of Technology, The Netherlands, 2000).
• Xu, L. and Wang, S. A. New generalized p-value and its upper bound for ANOVA under unequal error variances, Commun Stat Theory Methods 37, 1002–1010, 2008.
• Xu, L. and Wang, S. A. A new generalized p-value for ANOVA under heteroscedasticity, Statistics & Probability Letters 78 (8), 963–969, 2008.