By G. Dunn
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P characters, to unity, when they match on every character. Since this coefficient involves only the total number of matches (whether they are 1s or Os), it is particularly useful when it is considered that a match for Os conveys the same amount of information as a match for Is, as, for example, when the Is and Os are used merely as convenient labels for two alternative states of a character such as red and white. However, if a 1 is used to indicate the presence of some feature and 0 its absence, it may be necessary to consider alternative measures, such as Jaccard's coefficient, which exclude negative matches.
Yet a positive character such as the presence of wings (or flying organs defined without qualifications as to kind of wing) could mislead equally when considered for a similarly heterogeneous assemblage (for example, bat, heron and dragonfly). Neither can we argue that absence of a character may be due to a multitude of causes and that matched absence in a pair ofOTUs is therefore not 'true resemblance', for, after all, we know little more about the origins of matched positive characters. Such comments imply that each particular application must be considered on its merits and that no absolute statement can be made on whether or not to include 'negative' matches, although Sokal & Sneath (1963) suggest that a reasonable and logically defensible position appears to be the inclusion of positive and negative matches for those characters which vary within the group under study.
When one moves on to consider the comparison of groups the problems become more difficult. 7 (a) The choice ofa summary statisticfor each character to describe a group or population. This might be a proportion(s) (qualitative characters) or mean value (quantitative characters). (b) Measurement of within-group variation. (c) Construction of a measure of similarity or distance based on (a), and perhaps making allowance for (b). Making allowance for within-group variation might be particularly tricky if this is not constant from one group to another, and there is no reason to believe that it should be.
An Introduction to Mathematical Taxonomy by G. Dunn