Statistical Methods for Comparison of Forms - An Invariant Approach to Statistical Analysis of Shapes - page 172

careful to preserve the horizontal and vertical scales of the scatter plot
so that perceptions of influence are consistent from one plot to anoth-
er (Cole and Richtsmeier, 1998).
Additional visualization tools suggested by Cole and Richtsmeier
(1998) are best described using example data sets. In the following sec-
tion, we explore the data sets introduced in chapter 1 using these tools.
4.12 Analysis of example data sets: mouse mandibles
In Chapter 1 , we introduced the Ts65Dn mouse model for Down
Syndrome. The three-dimensional coordinates of the normal and
Ts65Dn mandibular data sets are presented in Chapter 3 . Here, we use
the methods outlined in the earlier part of this chapter to compare a
sample of Ts65Dn mice mandibles (N=7) with a sample of normal lit-
termates (N=13).
Form difference matrix
In this example, the mean form estimated from the normal mouse
mandible is used as the numerator, and the estimated mean form of the
Ts65Dn mandible is used as the denominator in an EDMA-I analysis.
The null hypothesis is that the shapes of the two mean forms are simi-
lar. The form difference matrix is presented in matrix format ( Table
4.2 ). Since the form difference matrix is symmetric, we present only the
diagonal elements (all equal to zero) and lower off-diagonal elements.
Observations can be made by simple inspection of the form differ-
ence matrix. For example, it is easy to see that elements that are
greater than one far out number elements that are less than one. This
means that the normal mandible is generally larger than the Ts65Dn
mandible along most dimensions. It also appears that many of the lin-
ear distances that have landmark 1 as an endpoint (look to the column
labeled LND 1) are of relatively greater magnitude than elements
associated with other landmarks.
Inspecting the form difference matrix in this way is not systematic
and can become tedious, especially as the number of landmarks
increases. One way to look for patterns among the linear distances in
terms of their contribution to the difference in forms is to calculate con-
fidence intervals for the linear distances.