Statistical Methods for Comparison of Forms - An Invariant Approach to Statistical Analysis of Shapes - page 193

provides such a scatter plot for the comparison of the Ts65Dn and nor-
mal mouse mandibles using all eleven landmarks. Landmark numbers
are written along the horizontal axis while values of the off-diagonal
elements of the form difference matrix (the form difference ratios) are
on the vertical axis. Remember that since the form difference matrix is
a square, symmetric matrix, the ratio for each linear distance appears
twice. The value of any particular ratio will appear once in the column
for each landmark that marks an endpoint of any linear distance.
In our example, the greatest dispersion of matrix values associated
with a single landmark is seen local to landmark 1. If we substitute an
alternate symbol for ratios corresponding to linear distances that have
landmark 1 as an endpoint, the influence of landmark 1 to the form dif-
ference becomes even more obvious ( Figure 4.11b ) . The largest matrix
values associated with landmarks 4 through 11 involve landmark 1,
and the smallest matrix values associated with landmarks 3 and 4
involve landmark 1. Visual inspection of this scatter plot provides the
researcher with evidence to pursue the role of landmark 1 in determin-
ing the difference between these two populations of forms.
Figure 4.11 Graph of the results of an EDMA comparison of the Ts65Dn aneuploid
mandibles with their normal littermates shown on a scatter plot. The Y-axis represents
the value of the elements of the form difference matrix while landmark numbers are
shown along the X-axis. The ratio value for the comparison of each linear distance is
shown twice on the graph, once for each landmark that is an endpoint for the linear dis-
tance. Figure 4.11a shows that the largest range of ratio values are associated with
linear distances that have landmark 1 as an endpoint. In Figure 4.11b all ratios associ-
ated with linear distances that have landmark 1 as an endpoint are graphed as closed
diamonds showing that the outlying values (in either the direction greater than or less
than 1) for each landmark map to the distance between that landmark and landmark 1.