Geoscience Reference
In-Depth Information
phrased, a test may pick up “departures” from
H
0
that result from “noise”
rather than real differences. Matloff (1991) describes how confidence interval
analysis may partly solve these problems. An advanced account of these topics
is given in Thompson (1992) and Krishnaiah and Rao (1988).
MATRIX FACILITIES: ANALYZING SEQUENTIAL DATA
A matrix is any rectangular array of numbers (e.g., frequencies, number of
transitions). If the array has
r
rows and
s
columns it is called an
r
by
s
(
r
´
s
)
matrix. Thus for example,
a
11
a
12
a
13
a
11
a
12
a
13
´
´
A (3
3)
a
21
a
22
a
23
and
B (2
3)
a
21
a
22
a2
3
a
31
a
32
a
33
where each row can represent the actor entry and columns the receiver; that is,
the value
a
11 represents frequency (or other value) of relations between the
row descriptor (
r
1) and the column descriptor (
s
1).
Our task here is not to explain the mathematical principles of matrices (see
Roberts 1992), but to describe their uses in behavioral sciences. Interaction
frequencies among individuals, presented as a sociometric matrix, are often the
basis for analysis of social dynamics. Individuals are classed as actors or initia-
tors in the rows (
r
) of the matrix and as receivers in the columns (
s
).
Other sociometric matrices include distance and association matrices; in
these, each cell contains a symmetric (dis)similarity measure for the pair of ani-
mals indicated by the row and the column of the cell. The cells of a transition
matrix contain the frequencies with which the behavior indicated by the row
(the preceding behavior) is followed by the behavior indicated by the column
(the succeeding behavior) (de Vries et al. 1993).
Relationships are often presented in terms of the dyadic interactions
between two individuals of the group. Frequencies of interactions within the
dyad during defined time intervals are then written in sociometric matrices.
These types of sociometric matrices are often used to identify the dominance
hierarchy among individuals based on such key behavior patterns as initiating
aggression. One individual is defined as a dominant (the winner), the other as
a subordinate (the loser). The strength of the relationship is expressed in terms
of linearity (Appleby 1983). Han de Vries (1995) developed an improved test
of linearity in dominance hierarchies containing unknown or tied relation-
