Russel-Research-Method-in-Anthropology

Multivariate Analysis 683
instead of in only two. The extra dimension would give us plenty of room to
move around and we could better adjust the proportionality of the distances
between the various pairs of variables.
In principle, you can perfectly represent the relations among n variables in
n 1 dimensions, so that any graph of six variables can be perfectly represented
in five dimensions. But even a three-dimensional graph is hard to read.
What would you do with a five-dimensional graph?
Most researchers specify a two-dimensional solution when they run an
MDS computer analysis. MDS programs produce a statistic that measures the
‘‘stress’’ in the graph produced by the program. This is a measure of how far
off the graph is from one that would be perfectly proportional. The lower the
stress, the better the solution. This means that a cluster of variables in an MDS
graph with low stress is likely to reflect some reality about the cognitive world
of the people being studied.
A Physical World Example: Making Maps with MDS
A physical example, based on metric data, will make this clearer. Afterward,
we’ll move on to a cognitive example, one based on nonmetric data.
Table 21.26 shows the road distance in miles between all pairs of nine cities
in the United States.
TABLE 21.26
Distances between Nine U.S. Cities (in Miles)
BOS NY DC MIA CHI SEA SF LA DEN
Boston 0
NY 206 0
DC 429 233 0
Miami 1504 1308 1075 0
Chicago 963 802 671 1329 0
Seattle 2976 2815 2684 3273 2013 0
SF 3095 2934 2799 3053 2142 808 0
LA 2979 2786 2631 2687 2054 1131 379 0
Denver 1949 1771 1616 2037 996 1037 1235 1059 0
SOURCE: Anthropac 4.0 and Anthropac 4.0 Methods Guide, by S. P. Borgatti, 1992a, 1992b. Reprinted with
permission of the author.
Note two things about the numbers in this table. First, the numbers are dissimilarities,
not similarities, because bigger numbers mean that things are farther
apart—less like each other. Smaller numbers mean that things are close
together—more similar. Similarity and dissimilarity matrices are known col-