Permutation tests for multi-factorial analysis of variance

Journal of Statistical Computation and Simulation

Volumn 73, Issue 2, 2003, Pages 85-113

  Anderson, Marti J ^a,c   Ter Braak, Cajo J F ^b  

^a UNIVERSITY OF SYDNEY   (Australia)

^b WAGENINGEN UNIVERSITY   (Netherlands)

^c UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

ANOVA; Experimental design; Fixed and random factors; Hierarchical designs; Mixed models; Non parametric; Randomization tests; Resampling methods

Indexed keywords

EID: 0037319490     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949650215733     Document Type: Article

References (51)

1. Anderson, M. J. (2001). A new method for non-parametric multivariate analysis of variance. Austral. Ecol., 26, 32-46.
2. Anderson, M. J. and Legendre, P. (1999). An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model. J. Statist. Comput. Simul., 62, 271-303.
3. Anderson, M. J. and Robinson, J. (2001). Permutation tests for linear models. Austral. & New Zealand J. Statist., 43, 75-88.
4. Boik, R. J. (1987). The Fisher-Pitman permutation test: a non-robust alternative to the normal theory F-test when variances are heterogeneous. Br. J. Math. Stat. Psychol., 40, 26-42.
5. Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. J. Amer. Statist. Assoc., 88, 9-25.
6. Brown, B. M. and Maritz, J. S. (1982). Distribution-free methods in regression. Austral. J. Statist., 24, 318-331.
7. Cade, B. S. and Richards, J. D. (1996). Permutation tests for least absolute deviation regression, Biometrics, 52, 886-902.
8. Clarke, K. R. (1993). Non-parametric multivariate analysis of changes in community structure. Austral. J. Ecol., 18, 117-143.
9. Cochran, W. G. (1974). Some consequences when the assumptions for the analysis of variance are not satisfied. Biometrics, 3, 22-38.
10. Crowley, P. H. (1992). Resampling methods for computation-intensive data analysis in ecology and evolution. Annu. Rev. Ecol. Syst., 23, 405-447.
11. Edgington, E. S. (1995). Randomization Tests, 3rd ed. Marcel Dekker, New York.
12. Excoffier, L., Smouse, P. E. and Quattro, J. M. (1992). Analysis of molecular variance inferred from metric distances among DNA haplotypes: application to human mitochondrial DNA restriction data. Genetics, 131, 479-491.
13. Fisher, R. A. (1935). Design of Experiments. Oliver and Boyd, Edinburgh.
14. Freedman, D. and Lane, D. (1983). A nonstochastic interpretation of reported significance levels. J. Bus. Econ. Statist., 1, 292-298.
15. Gaston, K. J. and McArdle, B. H. (1994). The temporal variability of animal abundances: measures, methods and patterns. Philos. Trans. R. Soc. London Ser. B, 345, 335-358.
16. Gonzalez, L. and Manly, B. F. J. (1998). Analysis of variance by randomization with small data sets. Environmetrics, 9, 53-65.
17. Good, P. I. (2000). Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses, 2nd ed. Springer-Verlag, Berlin.
18. Gower, J. C. and Krzanowski, W. J. (1999). Analysis of distance for structured multivariate data and extensions to multivariate analysis of variance. J. Roy. Statist. Soc. Ser. C Appl. Statist., 48, 505-519.
19. Hayes, A. F. (1996). Permutation test is not distribution free. Psychol. Methods, 1, 184-198.
20. Hope, A. C. (1968). A simplified Monte Carlo significance test procedure. J. Roy. Statist. Soc. Ser. B, 30, 582-598.
21. Hubert, L. and Schultz, J. (1976). Quadratic assignment as a general data analysis strategy. Br. J. Math. Stat. Psychol., 29, 190-241.
22. Johnson, C. R. and Field, C. A. (1993). Using fixed-effects model multivariate analysis of variance in marine biology and ecology. Oceanogy. Mar. Biol. Ann. Rev., 31, 177-221.
23. Kempthorne, O. (1952). The Design and Analysis of Experiments. John Wiley & Sons, New York.
24. Kempthorne, O. (1955). The randomization theory of experimental inference. J. Amer. Statist. Assoc., 50, 946-967.
25. Kempthorne, O. (1966). Some aspects of experimental inference. J. Amer. Statist. Assoc., 61, 11-34.
26. Kennedy, P. E. and Cade, B. S. (1996). Randomization tests for multiple regression. Commun. Statist. - Simulation Comput., 25, 923-936.
27. Liang, K.-Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
28. Manly, B. F. J. (1997). Randomization, Bootstrap and Monte Carlo Methods in Biology, 2nd ed. Chapman and Hall, London.
29. Mantel, N, and Valand, R. S. (1970). A technique of nonparametric multivariate analysis. Biometrics, 26, 547-558.
30. Mardia, K. V. (1971). The effect of non-normality on some multivariate tests and robustness to non-normality in the linear model. Biometrika, 58, 105-121.
31. McArdle, B. H. and Anderson, M. J. (2001). Fitting multivariate models to community data: a comment on distance-based redundancy analysis. Ecology, 82, 290-297.
32. McCullagh, P. and Neider, J. A. (1989). Generalized Linear Models, 2nd ed. Chapman and Hall, London.
33. Mielke, P. W., Berry, K. J. and Johnson, E. S. (1976). Multi-response permutation procedures for a priori classifications. Commun. Stat. - Theory and Methods A, 5(14), 1409-1424.
34. Nelder, J. A. (1964a). The analysis of randomized experiments with orthogonal block structure. I. Block structure and the null analysis of variance. Proc. Roy. Statist. Soc. Ser. A, 283, 147-162.
35. Nelder, J. A. (1964b). The analysis of randomized experiments with orthogonal block structure. II. Treatment structure and the general analysis of variance. Proc. Roy. Statist. Soc. Ser. A, 283, 163-178.
36. Nelder, J. A. and Wedderburn, R. W. M. (1972). Generalized linear models. J. Roy. Statist. Soc. Ser. A, 135, 370-384.
37. Olson, C. L. (1974). Comparative robustness of six tests in multivariate analysis of variance. J. Amer. Statist. Assoc., 69, 894-908.
38. Pesarin, F. (2001). Multivariate Permutation Tests: With Applications in Biostatistics. John Wiley and Sons, Chichester.
39. Pillar, V D. P. and Orlóci, L. (1996). On randomization testing in vegetation science: multifactor comparisons of relevé groups. J. Veg. Sci., 7, 585-592.
40. Pitman, E. J. G. (1937). Significance tests which may be applied to samples from any populations. III. The analysis of variance test. Biometrika, 29, 322-335.
41. Scheffé, H. (1959). The Analysis of Variance. John Wiley & Sons, New York.
42. Searle, S. R., Casella, G. and McCulloch, C. E. (1992). Variance Components. John Wiley & Sons, New York.
43. Smith, E. P., Pontasch, K. W. and Cairns, J. (1990). Community Similarity and the analysis of multispecies environmental data: a unified statistical approach. Water Res., 24, 507-514.
44. Snedecor, G. W. and Cochran, W. G. (1967). Statistical Methods, 6th ed. University of Iowa Press, Ames, Iowa.
45. Still, A. W. and White, A. P. (1981). The approximate randomization test as an alternative to the F test in analysis of variance. Br. J. Math. Stat. Psychol., 34, 243-252.
46. ter Braak, C. J. F. (1992). Permutation versus bootstrap significance test in multiple regression and ANOVA. In: Jöckel, K.-H., Rothe, G. and Sendler, W. (Eds.), Bootstrapping and Related Techniques. Springer-Verlag, Berlin, pp. 79-86.
47. ter Braak, C. J. F. and Šmilauer, P. (1998). CANOCO Reference Manual and User's Guide to Canoco for Windows: Software for Canonical Community Ordination (version 4). Micro Computer Power, Ithaca, New York.
48. Taylor, L. R. (1961). Aggregation and the mean. Nature, 189, 732-735.
49. Welch, W. J. (1990). Construction of permutation tests. J. Amer. Statist. Assoc., 85, 693-698.
50. Winer, B. J., Brown, D. R. and Michels, K. M. (1991). Statistical Principles in Experimental Design, 3rd ed. McGraw-Hill, New York.
51. Zeger, S. L. and Liang, K.-Y. (1992). An overview of the methods for the analysis of longitudinal data. Statistics in Medicine, 11, 1825-1839.