Information Technology Reference
In-Depth Information
Ta b l e 8 . 3 .
Preliminary calculations for a 3
×
2 ANOVA data set (
Y
ijk
matrix)
Large
Small
Rural
Large
Small
Rural
female
female
female male
male
male
a
1
b
1
a
2
b
1
a
3
b
1
a
1
b
2
a
2
b
2
a
3
b
2
15
38
42
16
28
10
20
43
48
22
34
16
10
33
36
10
22
4
21
46
49
21
35
15
9
30
35
11
21
5
AB
AB
jk
75
190
210
80
140
50
Y
2
Y
ijk
1,247
7,398
8,990
1,402
4,090
622
Y
jk
15.00
38.00
42.00
16.00
28.00
10.00
s
jk
5.52
6.67
6.52
5.52
6.52
5.52
AB
matrix (sums):
Size of residence community
Gender
Large (
a
1
)
Small (
a
2
)
Rural (
a
3
) Marginal sum
Female (
b
1
)
75
190
210
475
Male (
b
2
)
80
140
50
270
Marginal sum
155
330
260
745
AB
matrix (means):
Size of residence community
Gender
Large (
a
1
)
Small (
a
2
)
Rural (
a
3
) Marginal sum
Female (
b
1
)
15.00
38.00
42.00
31.67
Male (
b
2
)
16.00
28.00
10.00
18.00
Marginal sum
15.50
33.00
26.00
of Table 8.3. Also provided in Table 8.3 is an
AB
matrix of sums that we will
also be using in our computation of the sums of squares. The
AB
matrix
of means (at the bottom of Table 8.3) is useful when plotting treatment
means or examining simple effects analyses.
We are now ready to proceed with the analysis. You can examine
Table 8.3 to see where the actual values we are using in the computa-
tional formulas come from. We owe a special debt of thanks for the early
work by Keppel (1991), Keppel et al. (1992), and Keppel and Wickens
(2004) on the development of the computational formulas we are about to
use.
8.7.2 CALCULATING SUM OF SQUARES
There are five sums of squares to be calculated in a two-way between-
subjects ANOVA:
Sum of squares main effect of Factor
A
(
SS
A
).
Sum of squares main effect of Factor
B
(
SS
B
).
Sum of squares interaction effect of Factors
A
and
B
(
SS
A
×
B
).
