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Distances, like correlations, can be used to indicate the similarity between a pair of constructs (with respect to their common elements) or a pair of elements (with respect to their common constructs). However these two measures differ in a number of respects: they pay attention to different aspects of the similarity of the profiles of scores (see correlations for details), one (distances) is formed in terms of differences (one rating is subtracted from the other), the other in terms of cross-products (one rating is multiplied by the other), and distances are not reported on a common scale, being a transformation of the scale of the original ratings. There are a number of forms of distance: most commonly used in grid work are city-block or Euclidean distances (although other more arcane variants, such as Minkowski distances, can be used through standard statistical packages such as SPSS). The city block distance is the sum of the absolute (ie the sign is ignored) differences between ratings, so called because it corresponds to the distance one has to travel between locations in a city with a rectangular grid for a street plan (such as Manhattan or Melbourne). It is the exact inverse of a matching sum for binary data. City-block distances are the basis for the cluster analysis procedure in the FOCUS programme. Euclidean distance is the straight line between points variety (or ‘as the crow flies’).
Richard C. Bell

Establ. 2003
Last update: 15 February 2004