Biology Reference
In-Depth Information
variable”. The important characteristic of these variables is that they are not measured nor
arrayed in a sequence; they do not have intrinsic numerical values, nor do they have an
inherent order or sequence.
Sometimes, features that can be scored on a continuous graded scale are treated as cate-
gorical variables. For example, the proportions of meat and vegetation in an animal's diet
can be quantified and scored along a continuum. Nevertheless, it is a common practice to
sort diets into a small number of categories (e.g. carnivore, herbivore, omnivore). Other
traits that might be treated in a similar fashion include geographic location and age. There
are several reasons for treating these kinds of traits as categorical variables. One is a lack
of sufficient information to justify or support a more finely graded analysis
for example,
a researcher may not have precise data on the proportions of food items in the diets of all
species or individuals in a study. Another reason for treating a quantifiable trait as a cate-
gorical variable is that the investigator may not want to impose a hypothesis of ordering
on the data, which is often a consideration when groups are not dispersed along a single
straight line. Similarly, the investigator may not want to assume that all steps are of equal
value (e.g. ontogenies often can be divided into discrete instars or age classes based on
sequences of developmental events, but the sequentially numbered steps may represent
different amounts of time or ontogenetic change). Under these circumstances, a quantifi-
able trait may be treated as a categorical variable and CVA would then be used to describe
differences among the groups delineated by distinct states. However, the user should be
aware that taking this approach also limits the inferences that can be drawn from the
result
for example, an observation that age classes can be differentiated does not neces-
sarily imply the kind of monotonic progression from age to age that can be inferred from
a regression.
Geometric Description of CVA
To develop a geometric intuition for CVA, we return to the metaphor of a slightly flat-
tened watermelon. In PCA, we described the positions of seeds within the watermelon by
finding its greatest dimensions. In CVA, we are not interested in the positions of seeds in
the watermelon; instead, we want to describe the positions of the watermelons in the field
(centroids of the ellipses in
Figure 6.10
). If all we want to know is the location of each
FIGURE 6.10
Ellipses of variation in two
dimensions (
X
1
and
X
2
) for four sample
populations. Stars indicate locations of the
means of each sample.
X
1
