Statistical Methods for Comparison of Forms - An Invariant Approach to Statistical Analysis of Shapes - page 187

Most confidence intervals excepting those that have landmarks 1 or 2 as
an end point include zero within the confidence interval. This result
localizes differences in shape to two landmarks, the coronoid process
(landmark 1) and the mandibular angle (landmark 2).
A non-statistical approach to exploring the shape or form
difference
Simple inspection of the form difference matrix written as a sorted vec-
tor (see section for testing the null hypothesis using EDMA-I above)
makes certain observations evident. First, the two smallest values
within the form different matrix are considerably smaller than any
other values in the matrix. Second, these two values are associated
with linear distances that share landmark 1 as an endpoint. Third, the
normal mouse (the numerator sample) is equal to or larger than the
Ts65Dn mouse for all other linear distances. This informs us that the
distance between landmarks 1 and 3 and landmarks 1 and 4 are
markedly different between the two samples, but also differ from the
overall pattern of form difference between the samples.
Look now to the other extreme of the vector. Landmark 1 also
appears as an endpoint for many of the linear distances that have rel-
atively large magnitudes. Since the normal mouse is being used as the
numerator in this calculation, linear distances at this end of the matrix
are relatively larger in the mandibles of the normal mice. Clearly, land-
mark 1 is being revealed as a landmark that is influential to the
difference between the mandibular morphology of these two popula-
tions. Our goal is to explain how some linear distances that have
landmark 1 as an endpoint are smaller than normal in the Ts65Dn
mandible while others are larger than normal.
Pictures of the mean forms can be helpful in interpreting this out-
put. Consider Figure 4.10. In this figure we indicate those linear
distances associated with landmark 1 that are larger in the Ts65Dn
aneuploid mandible (from 1 to 3 and from 1 to 4) using a bold line.
Those linear distances associated with landmark 1 that are smaller in
the Ts65Dn aneuploid mandible are shown using a thin line.
Landmark 1 is located on the apex of a process that is a site of attach-
ment for one of the larger muscles of mastication. Linear distances
originating from the coronoid process (landmark 1) and stretching
along a posteroinferior axis are larger, while linear distances originat-
ing at landmark 1 but stretching along an anteroinferior axis are
smaller in the Ts65Dn mandible. We propose that a local change in the