Biology Reference
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Figure 3.5. A hypothetical example of landmark data whose proximity and local vari-
ability cause landmarks to swap relative locations during statistical analysis
prohibiting statistical testing. When EDMA is applied and the model-based bootstrap-
ping method is chosen for statistical testing (see Chapter 4 ), hypothetical forms are
generated from the mean form and variance-covariance matrix. When the variability
around a landmark is large and landmarks are placed relatively close to one another,
as in the center of this figure, two landmarks can change relative positions preventing
statistical testing.
first molar is available, while in other individuals only a left first molar
is available, these can be combined into a single sample if symmetry of
the biological organisms can be assumed and if the methods used are
reflection invariant. Of course the biologist will keep records of the col-
lected data and have knowledge of which specimens were reflected for
analysis. The concept of reflection invariance can be useful mathemat-
ically, statistically, and biologically.
Nuisance parameters and variance estimation. We have proposed a
method for estimating the mean form and the variability of forms with-
in a single population using the Euclidean Distance Matrix
representation of the form of an object. An alternate method for the
estimation of the mean form and variability of forms within a single
population is based on Procrustes superimposition (Goodall, 1991).
 
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