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our observed
F
value exceeds the critical value of
F
,werejectthenull
hypothesis and conclude that there are statistically significant differences
among the female residential size loneliness scores.
This statistically significant
F
should be followed up with planned
or unplanned (post hoc) comparisons. We refer you to our previous
discussions in Chapter 7 for the computational details of these analyses.
Remember to substitute
MS
S
/
AB
and
df
S
/
AB
for
MS
S
/
A
and
df
S
/
A
in the
Tukey and LSD formulas of Equations 7.5 and 7.6.
8.8.2 SIMPLE EFFECTS OF
A
AT
b
2
(
AB
j
2
)
2
n
(
B
2
)
2
(
a
)(
n
)
SS
A
at
b
2
=
−
(80)
2
(140)
2
(50)
2
(270)
2
(3)(5)
+
+
=
−
(5)
28,500
5
72,900
15
=
−
=
5,700
−
4,860
=
840.00
(8.10)
df
A
at
b
2
=
a
−
1
=
3
−
1
=
2
(8.11)
SS
A
at
b
2
840
.
00
MS
A
at
b
2
=
df
A
at
b
2
=
=
420.00
(8.12)
2
MS
A
at
b
2
MS
S
/
AB
=
420
.
00
F
A
at
b
2
=
=
11.40
.
(8.13)
.
36
83
Our evaluation criteria for this simple effect analysis remains the same
as the previous analysis because the degrees of freedom remain unchanged.
Thus, we conclude that this observed
F
is statistically significant, indicating
loneliness differences among the three residential community groups for
males. Again, planned or post hoc comparisons should be conducted next
to determine what is producing the interaction effect observed with our
omnibus ANOVA.
One last computational note: If the interaction in your omnibus
ANOVA is not statistically significant, but one or both of your main
effects is statistically significant, you could perform the following LSD
post hoc tests on the marginal sums of
A
or
B
.
D
LSD
−
A
(significant main effect of A)
F
(1,
df
S
/
AB
)
(2)(
b
)(
n
)(
MS
S
/
AB
)
=
.
(8.14)
D
LSD
−
B
(significant main effect of B)
F
(1,
df
S
/
AB
)
(2)(
a
)(
n
)(
MS
S
/
AB
)
=
.
(8.15)
