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.
E. the Y variables) account for most of the variation, it might be possible to use only these in subsequent analyses and thus achieve a considerable simplification. 3 by a brief mathematical account. 1, and clearly the pairs of measurements are highly correlated. H one wished to express the variation in these two characters on a single axis or dimension, what would be the 'best' axis to choose? One intuitively sensible answer to this question would be to choose the axis which maximizes the variance of the projections of the four points onto itself, since this will provide the maximum discrimination between the four buttercups.
12) The shape coefficient, Ci, looks formidable but is essentially nothing more than the variance of the differences in the character states of the OTUs being compared. It is likely to be large when considerable discrepancy in the magnitude of the differences occurs, including a mixture of positive, negative and negligible terms. The size coefficient, C~, will be large when the character states of the two OTUs are quite different in magnitude, and the differences are largely in one direction. For example, a large C~ value would arise if one OTU was very similar to another but much larger along most of the character scales.