The Index-of-Dispersion Test Revisited

  • D. Pfeifer
  • H. Ortleb
  • U. Schleier-Langer
  • H.-P. Bäumer
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


In quantitative ecology the classical index-of-dispersion is widely used for testing the hypothesis of spatial randomness. However, spatial aggregation of individuals is often observed in field experiments, so that the test will frequently reject the hypothesis without indicating any alternatives. In this paper we consider a modified index-of-dispersion test which allows for testing the hypothesis of a spatial Poisson point process with intensity measure having a density λ(x) of the form
$$ \lambda (x)\, = \,\sum\limits_{j = 1}^n {a_i f_j (x),\,\,\,x \in \mathbb{R}^2 } $$
with known non-negative regression functions f j (x) and unknown non-negative parameters a j which are to be estimated by the observed data. This model includes the classical case for n = 1 and f 1(x) = 1. Further applications to testing local geographical influences on health data are also pointed out.


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  1. APPELRATH, H.-J., BEHRENDS, H., JASPER, H., ORTLEB, H. ET AL. (1993): Endbericht der Projektgruppe”Aktive Informationssysteme”, Bericht IS 15, Teil A. Fachbereich Informatik, Universität Oldenburg.Google Scholar
  2. DIGGLE, P.J. (1983): Statistical Analysis of Spatial Point Patterns. Mathematics in Biology. Ac. Press, N.Y.Google Scholar
  3. EKSCHMITT, K. (1993): Über die räumliche Verteilung von Bodentieren. Zur ökologischen Interpretation der Aggregation und zur Probenstatistik. Dissertation, Universität Bremen.Google Scholar
  4. FAHRMEIR, L., AND HAMERLE, A. (Eds.) (1984): Multivariate statistische Verfahren. W. de Gruyter, Berlin.Google Scholar
  5. GARDNER, M.J. (1993): Investigating childhood leukaemia rates around the Sellafield nuclear plant. Int. Stat. Rev. 61, 231–244.CrossRefGoogle Scholar
  6. GREIG-SMITH, P. (1983): Quantitative Plant Ecology. Studies in Ecology, Vol. 9. 3rd edition, Blackwell Scientific Publ., Oxford.Google Scholar
  7. KAFADAR, K., AND TUKEY, J.W. (1993): U.S. cancer death rates: a simple adjustment for urbanization. Int. Stat. Rev. 61, 257–281.CrossRefGoogle Scholar
  8. KREBS, C.J. (1985): Ecology. The Experimental Analysis of Distribution and Abundance. 3rd edition, Harper & Row, N.Y.Google Scholar
  9. PFEIFER, D., BÄUMER, H.-P., AND ALBRECHT, M. (1992): Spatial point processes and their applications to biology and ecology. Modeling of Geo-Biosphere Processes 1, 145–161.Google Scholar
  10. PFEIFER, D., SCHLEIER-LANGER, U., AND BÄUMER, H.-P. (1994): The analysis of spatial data from marine ecosystems. To appear in: H.-H. Bock, W. Lenski, and M.M. Richter (eds.): Information Systems and Data Analysis. Prospects – Foundations – Applications. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, N.Y.Google Scholar
  11. REISE, K. (1985): Tidal Flat Ecology. An experimental approach to species interactions. Ecological Studies 54, Springer, N.Y.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1996

Authors and Affiliations

  • D. Pfeifer
  • H. Ortleb
  • U. Schleier-Langer
    • 1
  • H.-P. Bäumer
    • 2
  1. 1.Fachbereich Mathematik, Carl von OssietzkyUniversität OldenburgOldenburgGermany
  2. 2.Hochschulrechenzentrum, Carl von Ossietzky Universität OldenburgOldenburgGermany

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