Article: Cluster analysis of previously described communities from the Ludlow of the Welsh Borderland
Previously described communities (' associations') from the Ludlow of the Welsh Borderland were subjected to cluster analysis on a PC microcomputer. Miscellaneous absence-presence data sets derived from the published information were analysed using different combinations of clustering algorithms, distance and similarity measurements, with and without Jaccard's coefficient of association. Variations in order of data entry produced major differences (chaotic behaviour) in clustering using unmodified data. With unmodified data, only the single linkage method showed no clustering differences with the three distance and similarity measurements applied to the whole of the data. The raw data, modified with Jaccard's coefficient, showed major improvement in clustering upon variation of order of data entry. Such improvement in non-chaotic behaviour is interpreted as the result of the lesser, finite raw data consisting of zeros and ones, as compared with the more infinite numbers generated using a coefficient of association. Nearly equally good results are obtained, however, when the unmodified data are analysed using the cosine theta measurement. The UPGMA, single and complete linkage methods, with cosine theta, are recommended as quickly and routinely applicable to unmodified data for, at least, first approximations in community analysis. Dendrograms so generated should nonetheless be submitted to variation in order of data entry to test for chaotic behaviour.