Biology Reference
In-Depth Information
0.006
0.004
0.002
0.000
-0.002
-0.004
-0.006
-0.008
-0.010
-0.008
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
0.008
CV1
FIGURE 6.17
CV scores for the three geographic samples of squirrel jaws. Circles
5
western Michigan, gray
squares
eastern Michigan, triangles
southern states.
5
5
CVA: the CV is not a complete description of the difference between groups, it is just that
part of what differs between groups that varies least within groups.
Like PCA, CVA will compute a set of axes under the specified constraints, regardless of
whether the differences between groups are statistically significant. The optimal discrimi-
nator in a data set need not be a statistically significant discriminator, and a statistically
significant discriminator may not turn out to be particularly effective in assigning speci-
mens to groups. To determine how many CVs are effective discriminators, we employ
Bartlett's (1947)
test for differences in the value of Wilk's lambda (
is the
within-groups sum of squares divided by the total sum of squares (within-plus between-
groups):
Λ
). Wilk's
Λ
det
ðWÞ
det
det
ðWÞ
Λ
5
ðTÞ
5
(6.42)
ðW
1
BÞ
det
where det is the determinant of the matrix. Conveniently,
can be computed as the prod-
uct of the eigenvalues of
W
(
W
1
B
)
2
1
. Bartlett's test uses the following formula to estimate
a
Λ
2
test statistic:
χ
2
χ
52
ð
W
2
ð
P
B
1
Þ=
2
Þ
ln
Λ
(6.43)
2
1
