Biology Reference
In-Depth Information
TABLE 9.5
A Two-Way Fixed Factor Analysis of Variance: The Impact of Sex and Region on
Chipmunk Jaw Size
Source
SS
df
MS
F
P
Sex
45.57
1
45.57
22.357
0.000
Region
4.413
1
4.413
2.165
0.144
Sex
3
Region
0.113
1
0.113
0.056
0.814
Error
230.323
113
2.038
TABLE 9.6
A Two-Way Mixed Model Analysis of Variance: Fluctuating Asymmetry of Alpine Chipmunk
Jaw Size
Source
SS
df
MS
F
P
Individual
960.08
93
10.3234
18.103
0.0001
Sides
1.34
1
1.3357
2.342
0.129
Individual
Sides
53.04
93
0.57027
1.512
0.0089
3
Measurement error
70.91
188
0.37716
litter is the nested term (it is nested within diet). Because litter is nested within diet, we do
not find all values of “litter” for all levels of “diet”
litter 1, for example, is found only at
one level of “diet” (“liquid”) and similarly, litter 2 is found only at one level of “diet”
(“powder”). The model looks like this,
Y
A
B
ð
A
Þ
1
ε
(9.23)
5
1
There is no interaction term for a nested model because there are no independent contrasts
of the levels of B within differing levels of A, hence we have no way to estimate the interaction
between the factors. What this means is that we have no information about the impact of a
powdered diet on litter 1, nor of a liquid diet on litter 2 and we therefore cannot determine
whether litters respond differently to diets.
Table 9.7
shows a calculation of the sums of
squares, degrees of freedom and expected mean squares for a two-factor, nested design.
Table 9.8
lists the F-ratios for A and B for different combinations of fixed and random values
of A and B although, in the case of nested models, the nested term is almost invariably ran-
dom.
Table 9.9
shows the results of the analysis of diet's impact on deer mouse jaw size. Diet
does have a significant impact on jaw size when tested against the nested term “litter”.
Univariate Three Factor Model
In this case, we have distinct factors, A, B,andC. In addition to their main effects, we also
have the interaction terms: A
B, A
C, B
C and A
B
C. The model looks like this:
3
3
3
3
3
Y
A
B
C
A
B
A
C
B
C
A
B
C
1
ε
(9.24)
5
1
1
1
3
1
3
1
3
1
3
3
