Morphometric Data - An Invariant Approach to Statistical Analysis of Shapes - page 17

if an object lies within the predetermined size distribution of a popu-
lation. For example, the standard growth chart for infants plots the
mean and standard deviation for body length, body weight, and head
circumference against age. New data points can be plotted and evalu-
ated in terms of the population norms for these measures.
2.1.2 Groups of linear distances
Sets of linear distances can be designed to summarize a form ( Figure
2.1.b ). Linear distance data are collected using measuring tapes or
sticks, hand-held calipers or other anthropometric devices, or comput-
ed from the coordinates of landmarks. Univariate statistics enable the
study of each of the measures by itself. However, scientists often want
to study the relationships among these various measures. Two linear
measures can be combined as a ratio to provide an index of the rela-
tionship between these measures within a form (e.g., wing length and
breadth). Such indices are often referred to as measures of shape and
are commonly used in biology. (To learn more about the use of ratios in
biology see Atchley, Gaskins et al., 1976; Atchley, 1978; Mosimann and
James, 1979).
Multivariate statistical techniques enable the study of multiple
measurements by considering the relationships among them. The use-
fulness of these methods in the analysis of biological organisms was
quickly recognized and multivariate techniques gained popularity
among biologists by the late 1960s. The use of multivariate statistics
did more than offer a way to look at a combination of linear distances.
These methods also offered a way to simultaneously consider multiple
measurements representing variables of different types (e.g., morpho-
logical, ecological, nutritional, or life history measurements). There are
many excellent statistical texts that treat multivariate techniques (e.g.,
Mardia, Kent et al., 1979). Kowalski (1972) provides a clear summary
of multivariate techniques, as well as an informed cautionary note
regarding the potential scientific (biological) ambiguity of results and
the impact of this on interpretation and communication of results.
2.1.3 Outlines, surfaces and volumes
Outline data are two-dimensional representations of the boundary of a
form ( Figure 2.1.c ) . Examples of such data include the outlines of a