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1 February 2004 Applying randomization tests to cluster analyses
John C. Hunter, R. Alan McCoy
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Abstract

In applying randomization tests to hierarchical cluster analyses, we have noted a potentially misleading result: within a significant group, linkages are often identified as significant even when species are randomly distributed among the group's sites. We demonstrate this through a cluster analysis of a constructed matrix with two groups of 20 sites that share no species, and within each group species are randomly distributed among sites. A randomization test identified both of the groups and all linkages within them as significant, while the same test found all linkages non-significant in the cluster analysis of a matrix containing just one of the two groups of 20 sites. In general, a non-random distribution of species within a data set shortens linkages relative to distances in null distributions derived from randomized versions of the data. This confounds efforts to identify significant sub-groups within a significant group. However, the significance of sub-groups possibly could be tested by comparing linkage distances to a null distribution derived from the randomization and clustering of a sub-matrix containing only the sites within the larger group. In essence, this comparison tests the null hypothesis that within the significant group, sites represent random assemblages of species. When applied to actual data sets, an approach involving sequential randomization tests could allow the evaluation of all nodes in a classification, increasing the utility of randomization tests and strengthening the interpretation of groups produced by cluster analysis.

John C. Hunter and R. Alan McCoy "Applying randomization tests to cluster analyses," Journal of Vegetation Science 15(1), 135-138, (1 February 2004). https://doi.org/10.1658/1100-9233(2004)015[0135:ARTTCA]2.0.CO;2
Received: 29 September 2000; Accepted: 6 November 2003; Published: 1 February 2004
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KEYWORDS
classification
Null distribution
Permutation test
Resampling
vegetation
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