A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models

Computational Statistics and Data Analysis

Volumn 51, Issue 12, 2007, Pages 5731-5742

  Krishnamoorthy, K ^a   Lu, Fei ^a   Mathew, Thomas ^b  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

Fixed effects; Generalized F test; Generalized p value; Inter laboratory studies; Random effects; Welch test

Indexed keywords

COMPUTER SIMULATION; ERROR ANALYSIS; MATHEMATICAL MODELS; RANDOM PROCESSES;

GENERALIZED F TEST; GENERALIZED P-VALUE; INTERLABORATORY STUDIES; RANDOM EFFECTS; WELCH TEST;

ANALYSIS OF VARIANCE (ANOVA);

EID: 34547141824     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.09.039     Document Type: Article

References (25)

1. Bishop D.J., and Dudewicz E.J. Exact analysis of variance with unequal variances: test procedures and tables. Technometrics 20 (1978) 419-430
2. Brown M.B., and Forsythe A.B. Small sample behavior of some statistics which test the equality of several means. Technometrics 16 (1974) 129-132
3. Coombs W.T., Algina J., and Oltman D.O. Univariate and multivariate omnibus hypothesis tests selected to control Type I error rates when population variances are not necessarily equal. Rev. Ed. Res. 66 (1996) 137-179
4. Chen S.Y., and Chen H. Single-stage analysis of variance under heteroscedasticity. Comm. Statist. Simulation Comput. 27 (1998) 641-666
5. Dajani, A.N., 2002. Contributions to statistical inference for some fixed and random models. Ph.D. Dissertation, Department of Mathematics and Statistics, University of Maryland, Baltimore County.
6. Dajani, A.N., Mathew, T., 2003. Comparison of some tests in the one-way ANOVA with unequal error variances. ASA Proceedings of the Joint Statistical Meetings, pp. 1149-1155.
7. Gamage J., and Weerahandi S. Size performance of some tests in one-way ANOVA. Comm. Statist. Simulation Comput. 27 (1998) 625-640
8. Gerami, A., Zahedian, A., 2001. Comparing the means of normal populations with unequal variances. Proceedings of the 53rd Session of International Statistical Institute, Seoul, Korea.
9. James G.S. The comparison of several groups of observations when the ratios of population variances are unknown. Biometrika 38 (1951) 324-329
10. Kesselman H.J., and Wilcox R.R. The improved Brown and Forsythe test for mean equality: some things cannot be fixed. Comm. Statist. Simulation Comput. 28 (1999) 687-698
11. Krutchkoff, R.G., 1988. One-way fixed effects analysis of variance when the error variances may be unequal. J. Statist. Comput. Simulation 30, 259-271.
12. Lee S., and Ahn C.H. Modified ANOVA for unequal variances. Comm. Statist. Simulation Comput. 32 (2003) 987-1004
13. Lee S.M.N. Optimal choice between parametric and nonparametric bootstrap estimates. Math. Proc. Cambridge Philos. Soc. 115 (1994) 335-363
14. Li B.W., and Cardozo M.S. Determination of total dietary fiber in foods or products with little or no starch, nonenzymatic-gravimetric method: collaborative study. J. Assoc. Anal. Chemists Internat. 77 (1994) 687-689
15. Mehrotra D.V. Improving the Brown and Forsythe solution to the generalized Behrens-Fisher problem. Comm. Statist. Simulation Comput. 26 (1997) 1139-1145
16. Moore D.S. The Basic Practice of Statistics (2003), Freeman, NY
17. Moser B.K., Stevens G.R., and Watts C.L. The two-sample t test versus the Satterthwaite's approximate F test. Comm. Statist. Theory Methods 18 (1989) 3963-3975
18. Rice W.R., and Gaines S.D. One-way analysis of variance with unequal variances. Proc. Nat. Acad. Sci. 86 (1989) 8183-8184
19. Rukhin A.L., and Vangel M.G. Estimation of a common mean and weighted means statistics. J. Amer. Statist. Assoc. 93 (1998) 303-308
20. Seber G.A.F. Linear Regression Analysis (1977), Wiley, NY
21. Vangel M.G., and Rukhin A.L. Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies. Biometrics 55 (1999) 129-136
22. Weerahandi S. ANOVA under unequal error variances. Biometrics 51 (1995) 589-599
23. Weerahandi S. Exact Statistical Methods for Data Analysis (1995), Springer, NY
24. Welch B.L. The generalization of Student's problem when several different population variances are involved. Biometrika 34 (1947) 28-35
25. Welch B.L. On the comparison of several mean values: an alternative approach. Biometrika 38 (1951) 330-336