PERMANOVA, ANOSIM, and the Mantel test in the face of heterogeneous dispersions: What null hypothesis are you testing?

Ecological Monographs

Volumn 83, Issue 4, 2013, Pages 557-574

  Anderson, Marti J ^a   Walsh, Daniel C I ^a  

^a MASSEY UNIVERSITY   (New Zealand)

Author keywords

ANOSIM; Bray Curtis; Community composition; Dispersion; Dissimilarities; Homogeneity; Multivariate analysis; Null hypothesis; PERMANOVA; PERMDISP; Permutation test; Species abundances

Indexed keywords

COMMUNITY COMPOSITION; COMMUNITY STRUCTURE; CORRELATION; DATA SET; DISPERSION; HETEROGENEITY; MULTIVARIATE ANALYSIS; SIMULATION;

EID: 84891355477     PISSN: 00129615     EISSN: 15577015     Source Type: Journal    
DOI: 10.1890/12-2010.1     Document Type: Article

References (62)

1. Anderson, M. J. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecology 26:32-46.
2. Anderson, M. J. 2006. Distance-based tests for homogeneity of multivariate dispersions. Biometrics 62:245-253.
3. Anderson, M. J., et al. 2011. Navigating the multiple meanings of b diversity: a roadmap for the practicing ecologist. Ecology Letters 14:19-28.
4. Anderson, M. J., K. E. Ellingsen, and B. H. McArdle. 2006. Multivariate dispersion as a measure of beta diversity. Ecology Letters 9:683-693.
5. Anderson, M. J., R. N. Gorley, and K. R. Clarke. 2008. PERMANOVA+ for PRIMER: Guide to software and statistical methods. PRIMER-E, Plymouth, UK.
6. Anderson, M. J., and J. Robinson. 2003. Generalized discriminant analysis based on distances. Australian and New Zealand Journal of Statistics 45:301-318.
7. Anderson, M. J., and T. J. Willis. 2003. Canonical analysis of principal coordinates: a useful method of constrained ordination for ecology. Ecology 84:511-525.
8. Boik, R. J. 1987. The Fisher-Pitman permutation test: a nonrobust alternative to the normal theory F test when variances are heterogeneous. British Journal of Mathematical and Statistical Psychology 40:26-42.
9. Box, G. E. P. 1953. Non-normality and tests on variances. Biometrika 40:318-335.
10. 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 25:290-302.
11. Chapman, M. G., and A. J. Underwood. 1999. Ecological patterns in multivariate assemblages: information and interpretation of negative values in ANOSIM tests. Marine Ecology Progress Series 180:257-265.
12. Clarke, K. R. 1993. Nonparametric multivariate analyses of changes in community structure. Australian Journal of Ecology 18:117-143.
13. Clarke, K. R., and R. N. Gorley. 2006. PRIMER v6: User manual/tutorial. PRIMER-E, Plymouth, UK.
14. Clarke, K. R., and R. H. Green. 1988. Statistical design and analysis for a 'biological effects' study. Marine Ecology Progress Series 46:213-226.
15. Clarke, K. R., P. J. Somerfield, and M. G. Chapman. 2006. On resemblance measures for ecological studies, including taxonomic dissimilarities and a zero-adjusted Bray-Curtis coefficient for denuded assemblages. Journal of Experimental Marine Biology and Ecology 330:55-80.
16. Cochran, W. G. 1941. The distribution of the largest of a set of estimated variances as a fraction of their total. Annals of Eugenics 11:47-52.
17. Cochran, W. G. 1947. Some consequences when the assumptions for the analysis of variance are not satisfied. Biometrics 3:22-38.
18. Cochran, W. G. 1951. Testing a linear relation among variances. Biometrics 7:17-32.
19. Edgington, E. S. 1995. Randomization tests. Third edition. Marcel Dekker, New York, New York, USA.
20. Ellingsen, K. E., and J. S. Gray. 2002. Spatial patterns of benthic diversity: is there a latitudinal gradient along the Norwegian continental shelf? Journal of Animal Ecology 71: 373-389.
21. Feir-Walsh, B. J., and L. E. Toothaker. 1974. An empirical comparison of the ANOVA F-test, normal scores test and Kruskal-Wallis test under violation of assumptions. Educational and Psychological Measurement 34:789-799.
22. Fisher, R. A. 1925. Statistical methods for research workers. Oliver and Boyd, Edinburgh, UK.
23. Fisher, R. A. 1939. The comparison of samples with possibly unequal variances. Annals of Eugenics 9:174-180.
24. Glass, G. V., P. D. Peckham, and J. R. Sanders. 1972. Consequences of failure to meet assumptions underlying the fixed effects analyses of variance and covariance. Review of Educational Research 42:237-288.
25. Good, I. J. 1982. An index of separateness of clusters and a permutation test for its significance. Journal of Statistical Computation and Simulation 15:261-275.
26. Gower, J. C., and W. J. Krzanowski. 1999. Analysis of distance for structured multivariate data and extensions to multivariate analysis of variance. Applied Statistics 48:505-519.
27. Gray, J. S., K. R. Clarke, R. M. Warwick, and G. Hobbs. 1990. Detection of initial effects of pollution on marine benthos: an example from the Ekofisk and Eldfisk oilfields, North Sea. Marine Ecology Progress Series 66:285-299.
28. Hayes, A. F. 1996. Permutation test is not distribution free. Psychological Methods 1:184-198.
29. Horsnell, G. 1953. The effect of unequal group variances on the F-test for the homogeneity of group means. Biometrika 40: 128-136.
30. Legendre, P., and M. J. Anderson. 1999. Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs 69:1-24.
31. Legendre, P., and M.-J. Fortin. 2010. Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data. Molecular Ecology Resources 10:831-844.
32. Legendre, P., and E. D. Gallagher. 2001. Ecologically meaningful transformations for ordination of species data. Oecologia 129:271-280.
33. Legendre, P., and L. Legendre. 1998. Numerical ecology. Second English edition. Elsevier, Amsterdam, The Netherlands.
34. Manly, B. F. J., and R. I. C. C. Francis. 2002. Testing for mean and variance differences with samples from distributions that may be non-normal with unequal variances. Journal of Statistical Computation and Simulation 72:633-646.
35. Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Research 27:209- 220.
36. Mantel, N., and R. S. Valand. 1970. A technique of nonparametric multivariate analysis. Biometrics 26:547- 558.
37. Mardia, K. V., J. T. Kent, and J. M. Bibby. 1979. Multivariate analysis. Academic Press, New York, New York, USA.
38. McArdle, B. H., and M. J. Anderson. 2001. Fitting multivariate models to community data: a comment on distance-based redundancy analysis. Ecology 82:290-297.
39. McArdle, B. H., and M. J. Anderson. 2004. Variance heterogeneity, transformations and models of species abundance: a cautionary tale. Canadian Journal of Fisheries and Aquatic Sciences 61:1294-1302.
40. Mielke, P. W., K. J. Berry, P. J. Brockwell, and J. S. Williams. 1981. A class of nonparametric tests based on multiresponse permutation procedures. Biometrika 68:720-724.
41. Olson, C. L. 1974. Comparative robustness of six tests in multivariate analysis of variance. Journal of the American Statistical Association 69:894-908.
42. Olson, C. L. 1979. Practical considerations in choosing a MANOVA test statistic: a rejoinder to Stevens. Psychological Bulletin 86:1350-1352.
43. Pearson, E. S. 1931. The analysis of variance in cases of nonnormal variation. Biometrika 23:114-133.
44. Pillai, K. C. S. 1955. Some new test criteria in multivariate analysis. Annals of Mathematical Statistics 26:117-121.
45. Pillar, V. D. P., and L. Orló ci. 1996. On randomization testing in vegetation science: multifactor comparisons of relevé groups. Journal of Vegetation Science 7:585-592.
46. R Development Core Team. 2012. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org
47. Rencher, A. C. 1998. Multivariate statistical inference and applications. John Wiley and Sons, New York, New York, USA.
48. Romano, J. P. 1990. On the behavior of randomization tests without group invariance assumption. Journal of the American Statistical Association 85:686-692.
49. Seber, G. A. F. 1984. Multivariate observations. John Wiley and Sons, New York, New York, USA.
50. Smith, E. P., K. W. Pontasch, and J. Cairns. 1990. Community similarity and the analysis of multispecies environmental data: a unified statistical approach. Water Research 24:507- 514.
51. Snedecor, G. W. 1934. Calculation and interpretation of analysis of variance and covariance. Collegiate Press, Ames, Iowa, USA.
52. Stevens, J. 1979. Comment on Olson: Choosing a test statistic in multivariate analysis of variance. Psychological Bulletin 86:355-360.
53. ter Braak, C. J. F. 1986. Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67:1167-1179.
54. Tomarken, A. J., and R. C. Serlin. 1986. Comparison of ANOVA alternatives under variance heterogeneity and specific noncentrality structures. Psychological Bulletin 99: 90-99.
55. Torres, P. S., M. B. Quaglio, and V. D. P. Pillar. 2010. Properties of a randomization test for multifactor comparisons of groups. Journal of Statistical Computation and Simulation 80:1131-1150.
56. Underwood, A. J. 1981. Techniques of analysis of variance in experimental marine biology and ecology. Oceanography and Marine Biology: An Annual Review 19:513-605.
57. Underwood, A. J. 1997. Experiments in ecology: their logical design and interpretation using analysis of variance. Cambridge University Press, Cambridge, UK.
58. Verdonschot, P. F. M., and C. J. F. ter Braak. 1994. An experimental manipulation of oligochaete communities in mesocosms treated with chlorpyrifos or nutrient additions: multivariate analyses with Monte Carlo permutation tests. Hydrobiologia 278:251-266.
59. Warton, D. I. 2011. Regularized sandwich estimators for analysis of high-dimensional data using generalised estimating equations. Biometrics 67:116-123.
60. Warton, D. I., and H. M. Hudson. 2004. A MANOVA statistic is just as powerful as distance-based statistics, for multivariate abundances. Ecology 85:858-874.
61. Warton, D. I., S. T. Wright, and Y. Wang. 2012. Distancebased multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution 3:89- 101.
62. Welch, B. L. 1937. The significance of the difference between two means when the population variances are unequal. Biometrika 29:350-362.