By G. Dunn
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2. Here four fairly distinct groups or clusters of aphids can be seen. When it is thought that the ftrst two components are inadequate for representing the structure in the data, a further component score can be accommodated by making a three-dimensional 'ball and wire' model or by constructing stereographic plots (see Rohlf, 1968, for examples). ) . 2. ) variation in size which is of interest; consequently, if it is thought that the first principal component is a measure of size, as in the cases of the turtles and aphids discussed previously, then more information about the relevant structure amongst the OTUs might be obtained by plotting the second principal component against the third, rather than a plot of components one and two.
Principal components analysis thus leads to a set of p composite characters that are uncorrelated and are arranged in order of decreasing variance. 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?
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. First similarity and distance measures for qualitative characters will be introduced, and then those for quantitative characters.
An Introduction to Mathematical Taxonomy by G. Dunn