Statistical tests on two characteristics of the shapes of cluster diagrams. (English) Zbl 0652.62054
Summary: 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) \(m_ k\), the number of groups of \(k+1\) 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.
(1) S, the number of single objects previously ungrouped that are joined in the final stages of clustering, and (2) \(m_ k\), the number of groups of \(k+1\) 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.
MSC:
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 05A15 | Exact enumeration problems, generating functions |
| 62G10 | Nonparametric hypothesis testing |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Keywords:
dendrogram; hierarchical cluster analysis; shape; significance testing; cluster diagram; rooted planar tree; clustering procedure; Ecological applications; weed communitiesReferences:
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