
Distances 

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 crossproducts (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 cityblock 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. Cityblock 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


