Biology Reference
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Using the estimators of mean form and variance-covariance struc-
ture described above, we estimate the mean shapes for the two
populations and calculate the shape difference . In the example below,
we use the geometric mean of the distances among mandibular land-
marks as the scaling factor and standardize the form difference matrix
for a sample by dividing each entry by the scaling factor calculated for
that sample. The result is a mean shape matrix that is dependent upon
the choice of scaling factor. In other words, if a scientific reason exists
for choosing an alternate measure as a scaling factor (i.e., the length of
a particular linear distance), the mean shape matrix will change. The
null hypothesis that the shapes are similar is tested using a paramet-
ric Bootstrap (i.e., Monte Carlo) procedure (see previous description of
EDMA-II this section and Part 2 of this chapter).
This example uses the same landmark data from the Ts65Dn and
normal mandibles used in the EDMA-I example above. The mean form
matrices estimated for these samples were given in Chapter 2 . The
scaling variables for the two samples are:
Geometric mean for linear distances from the normal sample: 5.23902
Geometric mean for linear distances from the Ts65Dn sample: 4.98840
Difference in geometric means between samples: 0.25062
Dividing each entry of the mean form matrix estimated for each sam-
ple by the sample-specific scaling factors, we arrive at a shape matrix
for each sample.
Elements of the shape difference matrix represent the difference
between like-linear distances in the two samples:
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