Small sample properties of tests on homogeneity in one-way Anova and meta-analysis

Statistical Papers

Volumn 43, Issue 2, 2002, Pages 197-235

  Hartung, Joachim ^a   Argaç, Dog̃an ^a   Makambi, Kepher H ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Balanced and unbalanced sample sizes; Homogeneous and heterogeneous variances; Meta analysis; Nonnormality

Indexed keywords

EID: 0036556873     PISSN: 09325026     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00362-002-0097-8     Document Type: Article

References (23)

1. Asiribo, O., Gurland, J. (1990). Coping with variance heterogeneity. Commun. Statist. Theory Meth., 19, 4029-4048.
2. Böckenhoff, A., Hartung, J. (1998). Some corrections of the significance level in meta-analysis. Biometrical Journal, 40, 937-947.
3. Box, G. E. P. (1954). Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effect of inequality of variance in the one-way classification. Annals of Mathematical Statistics, 25, 290-403.
4. Brown, M. B., Forsythe, A. B. (1974). The small sample behavior of some statistics which test the equality of several means. Technometrics, 16, 129-132.
5. Chalmers, T. C. (1991). Problems induced by recta-analyses. Statistics in Medicine, 10, 971-980.
6. Cochran, W. G. (1937). Problems arising in the analysis of a series of similar experiments. J. Roy. Stat. Soc. Supp., 4, 102-118.
7. Conover, W. J., Iman, R. L. (1981). Rank transformations as a bridge between parametric and nonparametric statistics. American Statistician, 35, 124-129.
8. De Beuckelaer, A. (1996). A closer examination on some parametric alternatives to the ANOVA F-test. Statistical Papers, 37, 291-305.
9. Fligner, M. A. (1981). Comment on rank transformations as a bridge between parametric and nonparametric statistics. American Statistician, 35, 131-133.
10. Hardy, R. J., Thompson, S. G. (1998). Detecting and describing heterogeneity in meta-analysis. Statistics in Medicine, 17, 841-856.
11. Hartung, J., Knapp, G. (2000). On tests of the overall treatment effect in the meta-analysis with normally distributed responses. Statistics in Medicine, to appear.
12. James, G. S. (1951). The comparison of several groups of observations when the ratios of population variances are unknown. Biometrika, 38, 324-329.
13. Keselman, H. J., Wilcox, R. R. (1999). The 'improved' Brown and Forsythe test for mean equality: some things can't be fixed. Commun. Statist.-Simula., 28, 687-698.
14. Lehmann, E. L. (1975) Nonparametrics. Holden Day, San Francisco.
15. Lehmann, E. L. (1986) Testing Statistical Hypotheses. 2nd edn., Wiley, New York.
16. Li, Y., Shi, L., Roth, H. D. (1994). The bias of the commonly-used estimate of variance in meta-analysis. Commun. Statist. Theory Meth., 23, 1063-1085.
17. Mehrotra, D. V. (1997). Improving the Brown-Forsythe solution to the generalized Behrens-Fisher problem. Commun. Statist.-Simula., 26, 1139-1145.
18. Noether, G. E. (1981). Comment on rank transformations as a bridge between parametric and nonparametric statistics. American Statistician, 35, 129-130.
19. Normand, S. T. (1999). Meta-analysis: Formulating, evaluating, combining, and reporting. Statistics in Medicine, 18, 321-359.
20. Patel, J. K., Kapadia, C. P., Owen, D. B. (1976) Handbook of Statistical Distributions. Marcel Dekker, New York.
21. Scheffé, H. (1959) The Analysis of Variance. Wiley, New York.
22. Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330-336.
23. Whitehead, A., Whitehead, J. (1991). A general parametric approach to the recta-analysis of randomized clinical trials. Statistics in Medicine, 10, 1665-1677.