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Expressions involving optimal sign vectors are derived so as to yield two new applications. First, coefficient alpha for the sign-weighted composite is maximized in analogy to Lord's scale-independent solution with differential weights. Second, optimal sign vectors are used to define two groups of objects that are maximally distinct in terms of a function of the squared euclidean distances between groups. An efficient computing algorithm is described along with several examples.
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Woodward et al. (1979) studied this question.
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