Journal of Advanced Statistics
Modified Tests for Heteroscedastic Two-Way MANOVA
Download PDF (623.4 KB) PP. 1 - 16 Pub. Date: March 1, 2016
Author(s)
- Shengning Xiao*
Department of Mathematics, School of Science, Tianjin University, China - Jin-Ting Zhang
Department of Statistics and Applied Probability, National University of Singapore, Singapore
Abstract
Keywords
References
[1] G. A. F. Seber, Multivariate observations. John Wiley & sons, New York, 1984.
[2] R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, 5th ed. Prentice Hall, Englewood Cliffs, NJ, USA, 2002.
[3] N. H. Timm, Applied multivariate analysis. Springer, New York, 2002.
[4] C. A. Tsai and J. J. Chen, “Multivariate analysis of variance test for gene set analysis,” Bioinformatics, vol. 25, pp. 897–903, 2009.
[5] G. E. P. Box, “A general distribution theory for a class of likelihood criteria,” Biometrika, vol. 36, pp. 317–346, 1949.
[6] H. Levene, “Robust tests for equality of variances,” in Contributions to probability and statistics: Essays in honor of Harold Hotelling, I. Olkin, S. G. Churye, W. Hoeffding, W. G. Madow, and H. B. Mann, Eds. Stanford University Press, 1960, pp. 278–292.
[7] T. W. Anderson, An introduction to multivariate statistical analysis, 3rd ed. John Wiley & Sons, New York, 2003.
[8] J. Stevens, Applied multivariate statistics for the social sciences. Hillsdale, NJ: Erlbaum, 1986.
[9] S. W. Harrar and A. C. Bathke, “A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations,” Annals of the Institute of Statistical Mathematics, vol. 64, no. 1, pp. 135–165, 2012.
[10] J. T. Zhang and S. Xiao, “A note on the modified two-way MANOVA tests,” Statistics and Probability Letters, vol. 82, no. 3, pp. 519–527, 2012.
[11] J. T. Zhang, “Two-way MANOVA with unequal cell sizes and unequal cell covariance matrices,” Technometrics, vol. 53, no. 4, pp. 426–439, 2011.
[12] Y. Fujikoshi, “Two-way ANOVA models with unbalanced data,” Discrete Mathematics, vol. 116, pp. 315–334, 1993.
[13] Y. Fujikoshi, “Asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis,”Annals of the Institute of Statistical Mathematics, vol. 27, pp. 99–108, 1975.
[14] A. M. Kshirsagar, Multivariate Analysis. Marcel Decker, New York, 1972.
[15] R. R. Wilcox, “Adjusting for unequal variances when comparing means in one-way and two-way fixed effects ANOVA model,” Journal of Educational Statistics, vol. 14, no. 3, pp. 269–278, 1989.
[16] K. J. Harris, D. Catley, G. E. Good, N. J. Cronk, S. W. Harrar, and K. B. Williams, “Motivational interviewing for smoking cessation in college students: A group randomized trial,” Preventive Medicine, vol. 51, no. 5, pp.387–393, 2010.
[17] T. F. Heatherton, L. T. Kozlowski, R. C. Frecker, and K. O. Fagerström, “The fagerström test for nicotine dependence: a revision of the fagerström tolerance questionnaire,” British Journal of Addiction, vol. 86, no. 9, pp. 1119–1127, 1991.
[18] R. J. Wellman, J. R. DiFranza, J. A. Savageau, S. Godiwala, K. Friedman, and J. Hazelton, “Measuring adults’ loss of autonomy over cigarette use: The hooked on nicotine checklist,” Nicotine and Tobacco Research, vol. 7, no. 1, pp. 157–161, 2005.
[19] D. K. Hatsukami, J. R. Hughes, R. W. Pickens, and D. Svikis, “Tobacco withdrawal symptoms: An experimental analysis,” Psychopharmacology, vol. 84, no. 2, pp. 231–236, 1984.
[20] D. G. Nel and C. A. Van Der Merwe, “A solution to the multivariate Behrens-Fisher problem,” Communications in Statistics - Theory and Methods, vol. 15, no. 12, pp. 3719–3735, 1986.