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In-Depth Information
8.7.3 CALCULATING DEGREES OF FREEDOM
Below are the formulas for the degrees of freedom associated with each
sum of squares, and the simple computations involved based on our
numerical example:
df
A
=
a
−
1
=
3
−
1
=
2
df
B
=
b
−
1
=
2
−
1
=
1
df
A
×
B
=
(
a
−
1)(
b
−
1)
=
(3
−
1)(2
−
1)
=
(2)(1)
=
2
df
S
/
AB
=
(
a
)(
b
)(
n
−
1)
=
(3)(2)(5
−
1)
=
(3)(2)(4)
=
24
df
T
=
(
a
)(
b
)(
n
)
−
1
=
(3)(2)(5)
−
1
=
29
.
8.7.4 CALCULATING MEAN SQUARES AND
F
RATIOS
Mean squares are calculated by dividing each sum of squares by its respec-
tive degrees of freedom. Note that we do not calculate a mean square
total value. Three
F
ratios are calculated in a two-way between-subjects
ANOVA. These three
F
ratios assess the three sources of between-subjects
variability found in the study. Thus,
F
A
assesses the main effect of Factor
A
,
F
B
assesses the main effect of Factor
B
, and
F
A
×
B
assesses the interaction
effect. Each
F
ratio is formed by dividing the respective mean square by
the mean square error (
MS
S
/
AB
). The calculation of these mean squares
and
F
ratios follows:
SS
A
df
A
=
1,551.17
2
MS
A
=
=
775.59
SS
B
df
B
=
1,400.84
1
MS
B
=
=
1,400.84
SS
A
×
B
df
A
×
B
=
1,412.16
2
MS
A
×
B
=
=
706.08
SS
S
/
AB
df
S
/
AB
=
884
00
24
.
MS
S
/
AB
=
=
36.83
MS
A
MS
S
/
AB
=
775
.
59
F
A
=
=
21.06
36
.
83
MS
B
MS
S
/
AB
=
1,400.84
36
F
B
=
=
38.04
.
83
MS
A
×
B
MS
S
/
AB
=
706
.
08
F
A
×
B
=
=
19.17
.
36
.
83
8.7.5 EVALUATING THE
F
RATIOS
We test the null hypothesis for each of our three observed (calculated)
F
ratios by evaluating (or comparing) each
F
value with critical values of
F
