Biology Reference

In-Depth Information

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

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

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