Biology Reference
In-Depth Information
TABLE 9.2
Sums of Squares, Degrees of Freedom and Mean Squares for a 2 Way, Balanced Univariate
ANOVA
Source
SS
df
MS
NJ
P
I
i
5
1
ð
2
A
SS
A
5
y
i
2
y
Þ
I
2
1
S
A
/(I
2
1)
NI
P
J
2
B
SS
B
5
1
ð
y
j
2
y
Þ
J
1
SS
B
/( J
1)
2
2
J
5
N
P
I
1
P
J
2
A
3
B
SS
AB
5
1
ð
y
ij
2
y
i
2
y
j
1
y
Þ
(I
2
1)(J
2
1)
SS
AB
/( I
2
1)(J
2
1)
i
5
j
5
SS
error
5
P
1
P
1
P
J
N
I
2
Residual
1
ð
y
ijk
2
y
ij
Þ
IJ(N
1)
SS
error
/IJ(N
1)
2
2
i
5
j
5
k
5
5
P
1
P
1
P
N
I
J
2
Total
SS
total
1
ð
y
ijk
y
Þ
IJN
1
2
2
k
5
i
5
j
5
There are I levels of factor A, and J levels of factor B, with
N
specimens per cell. The expressions of the form y
i
indicate means
over all cells with level i (or j, or the combination ij), while y is the overall mean of all data.
TABLE 9.3
Terms of the F-Ratio for a Univariate Two Factor, Balanced Design
Source
A, B Fixed
A,B Random
A Fixed, B Random
A
MS
A
/MS
error
MS
A
/MS
AB
MS
A
/MS
AB
B
MS
B
/MS
error
MS
B
/MS
AB
MS
A
/MS
AB
A
B
MS
AB
/MS
error
MS
AB
/MS
error
MS
AB
/MS
error
3
TABLE 9.4
Estimates of the Variances Components for a Univariate Two Factor, Balanced Design
Source
A, B Fixed
A,B Random
A Fixed, B Random
A
(MS
A
2
MS
error
)/NJ
(MS
A
2
MS
AB
)/NJ
(MS
A
2
MS
AB
)/NJ
B
(MS
B
2
MS
error
)/NI
(MS
B
2
MS
AB
)/NI
(MS
B
2
MS
error
)/NI
AB
(MS
AB
2
MS
error
)/N
(MS
AB
2
MS
error
)/N
(MS
AB
2
MS
error
)/N
Error
MS
error
MS
error
MS
error
on average than males' jaws (74.18 mm vs 72.88 mm for females and males, respectively). In
contrast, region does not have a statistically significant impact on jaw size, nor is there any
stastistically significant interaction between sex and region. The analysis of fluctuating
asymmetry of chipmunk jaws shows that the interaction term (which is fluctuating asym-
metry) is statistically significant although the main effect of “Sides” is not (
Table 9.6
).
Univariate Two Factor Nested Model
In this case, one of the two factors, B, is nested within factor A, which we denote as
B(A). As an example of nesting, we earlier introduced the case of the deer mice that were
fed three diets, with all members of each litter being fed the same diet. Thus, in this case,
