Abstract
Two distribution-free permutation techniques are described for the analysis of ecological data. These methods are completely data dependent and provide analyses for the commonly-encountered completely-randomized and randomized-block designs in a multivariate framework. Euclidean distance forms the basis of both techniques, providing consistency with the observed distribution of data in many ecological studies.
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Abbreviations
- MRPP=:
-
Multiresponse permutation procedure
- MRBP=:
-
Ibid, randomized block analog
References
Austin, M. P. 1987. Models for the analysis of species response to environmental gradients. Vegetatio 69: 35–45.
Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H. & Tukey, J. W. 1972. Robust estimates of location: survey and advances. Princeton University Press, Princeton, N. J.
Berry, K. J. & Mielke, P. W. 1984. Computation of exact probability values for multi-response permutation procedures (MRPP). Commun. Statist. Simulation Comput. 13: 417–432.
Biondini, M. E., Bonham, C. D. & Redente, E. F. 1985. Secondary successional patterns in a sagebrush (Artemisia tridentata) community as they relate to soil disturbance and soil biological activity. Vegetatio 60: 25–36.
Brockwell, P. J., Mielke, P. W. & Robinson, J. 1982. On non-normal invariance principles for multi-response permutation procedures. Austral. J. Statist. 24: 33–41.
Dielman, T. E. 1984. Least absolute value estimation in regression models: an annotated bibliography. Commun. Statist. 13: 513–541.
Dietz, T., Frey, R. S. & Kalof, L. 1987. Estimation with cross-national data: robust and nonparametric methods. Amer. Soc. Rev. 52: 380–390.
Dodge, Y. 1987. An introduction to L1-norm based statistical data analysis. Comput. Statist. Data Anal. 5:239–253.
Hampel, F. R., Ronchetti, E. M., Bousseeuw, P. J. & Stahel, W. A. 1986. Robust statistics: The approach based on influence functions. Wiley, New York.
Harter, H. L. 1974–1976. The method of least squares and some alternatives I. Int. Statist. Rev. 42: 147–174; II. 42: 235–264; III. 43: 1–44; IV. 43: 125–190, 273–278; V. 43: 269–272; VI. 44: 113–159.
Huynh, H. 1982. A comparison of four approaches to robust regression. Psych. Bull. 92: 505–512.
Huynh, H. & Mandeville, G. K. 1979. Validity conditions in repeated measures designs. Psych. Bull 86: 964–973.
Mielke, P. W. 1984. Meteorological applications of permutation techniques based on distance functions. In: Krishnaiah, P. R. & Sen, P. K. (eds), Handbook of statistics. Vol. 4, pp. 813–830. Elsevier Science Publishers, Amsterdam.
Mielke, P. W. 1986. Non-metric statistical analysis: some metric alternatives. J. Statist. Plann. Inference 13: 377–387.
Mielke, P. W. 1987. L1, L2 and L∞ regression models: is there a difference? J. Statist. Plann. Inference 16: 430.
Mielke, P. W., Berry, K. J. & Johnson, E. S. 1976. Multiresponse permutation procedures for a priori classifications. Commun. Statist. — Theor. Meth. 5: 1409–1424.
Narula, S. C. & Wellington, J. F. 1982. The minimum sum of absolute errors regression: a state of the art survey. Int. Statist. Rev. 50: 317–326.
Redente, E. F., Doerr, T. B., Grygiel, C. E., Allderdings, E., Stark, J. M. & Biondini, M. E. 1982. Effect of plant species, soil material, and cultural practices upon plant establishment on succession. In: Redente, E. F. & Cook, C. W. (eds), Revegetation studies on oil shale related disturbances in Colorado, pp. 1–25. DOE/EV/0401806. Dept. Range Science, Colorado State University, Fort Collins, Colorado.
Rey, W. J. J. 1983. Introduction to robust and quasi-robust statistical methods. Springer-Verlag, Berlin.
Sala, O. E. & Lauenroth, W. K. 1982. Small rainfall events: and ecological role in semiarid regions. Oecologia 53: 301–304.
Soriano, A. & Sala, O. 1983. Ecological strategies in a Patagonian arid steppe, Vegetatio 56: 9–15.
Wu, L. 1985. Robust M-estimation of location and regression. In: Tuma, N. B. (ed.), Sociological methodology, pp. 316–388. Jossey-Bass, San Francisco.
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Biondini, M.E., Mielke, P.W. & Berry, K.J. Data-dependent permutation techniques for the analysis of ecological data. Vegetatio 75, 161–168 (1988). https://doi.org/10.1007/BF00045630
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DOI: https://doi.org/10.1007/BF00045630