Statistical tests on two characteristics of the shapes of cluster diagrams |
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Authors: | M. R. T. Dale J. W. Moon |
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Affiliation: | (1) Department of Botany, University of Alberta, T6G 2E9 Edmonton, Alberta, Canada;(2) Department of Mathematics, University of Alberta, T6G 2E9 Edmonton, Alberta, Canada |
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Abstract: | A cluster diagram is a rooted planar tree that depicts the hierarchical agglomeration of objects into groups of increasing size. On the null hypothesis that at each stage of the clustering procedure all possible joins are equally probable, we derive the probability distributions for two properties of these diagrams: (1)S, the number of single objects previously ungrouped that are joined in the final stages of clustering, and (2)mk, the number of groups ofk+1 objects that are formed during the process. Ecological applications of statistical tests for these properties are described and illustrated with data from weed communities of Saskatchewan fields.This work was supported by the Natural Sciences and Engineering Research Council of Canada. |
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Keywords: | Combinatorial enumeration Dendrogram Hierarchical cluster analysis Shape Significance testing |
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