Russel-Research-Method-in-Anthropology

682 Chapter 21
TABLE 21.25
Matrix of Association among Four Variables
A B C D
A X 0.5 0.8 0.3
B X 0.4 0.64
C X 0.35
D
X
.8
A
C
a.
.8
.4
A
.5
B
C
.35
b.
.4
.3
.5
.65
B
D
Figure 21.3. Two-dimensional plot of the relation among three variables (a) and
among four variables (b).
With just three variables, it is easy to plot these distances in proper proportion
to one another. For example, the physical distance between B and C is
twice that of A and C in figure 21.3a. In fact, figure 21.3a contains precisely
the same information as the inside box of table 21.25, but in graphic form.
With four variables, things get considerably more complicated. With four
variables, there are six relations to cope with. These relations are shown in the
large box of table 21.25. Only one two-dimensional graph (apart from rotations
and enlargements) can represent the relative distances among the six
relations in table 21.25. The graph is shown in figure 21.3b.
Figure 21.3b is a two-dimensional graph of six relations in almost proper
proportions. When we have only two dimensions to work with, it is often
impossible to achieve perfect proportionality in a graph of six relations. One
way out of this is to depict the six relations in table 21.25 in three dimensions,