By G. Dunn
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Them particularly attractive. 3) That is, the dissimilarity between i and j is independent of the direction in which it is measured, and must be positive provided the two OTUs are not coincident. 4) That is, dij will take some non-zero value if i and j are not the same OTU. 5) (d) Triangular inequality: Given three OTUs i, j and k, the dissimilarities between them satisfy the inequality ~~~+4 p~ The triangular inequality is also known as the metric inequality, and dissimilarity coefficients satisfying the above properties are known as metrics and generally referred to as distances rather than dissimilarities.
Rao (1964) gives a mathematical 'argument for this interpretation, and the interested reader is referred to Blackith & Reyment (1971) for a fuller discussion of this point. As a second example, a set of data described by Jeffers (1967) of 40 individual winged aphids will be considered. 2. 3. 50 Component Cumulative . 4. Latent vectors for first four components of winged aphid variables (Jeffers, 1967) Latent vectors for component Variable Length Width Fore-wing Hind-wing Spiracles Antenna! segment Antenna!
E. W = W 1 + W 2' where W 1 and W 2 are the usual (p x p) matrices of character sums-of-squares and cross-products for the two groups. When correlations between characters are slight, D2 will be similar to the squared Euclidean distance computed on the standardized data. The use of D2 implies that the investigator is willing to assume that the character dispersions are at least approximately the same in the two groups. When this is not so D2 is inappropriate, and in such a case a possible alternative is Jardine and Sibson's Normal Information Radius (see Jardine & Sibson, 1971).