Information Technology Reference
In-Depth Information
Differences of Least Squares Means
This Table
presents both the
unadjusted
Standard
Error
Time_Recode Time_Recode
Estimate
DF
t Value
Pr
>
⏐
t
⏐
Adjustment
Adj P
Effect
Time_Recode
Time_Recode
Time_Recode
Time_Recode
Time_Recode
Time_Recode
Time_Recode
Time_Recode
Time_Recode
Time_Recode
-
value and the
Bonferroni
adjustment.
p
T1_pre1
T1_ pre1
T1_ pre1
T1_ pre1
T2_ pre2
T2_ pre2
T2_ pre2
T3_ post1
T3_ post1
T4_ post2
28
28
28
28
28
28
28
28
28
28
0.19
4.27
6.01
6.20
4.07
5.82
6.01
1.75
1.94
0.19
0.8477
0.0002
<.0001
<
T2_ pre2
T3_ post1
T4_ post2
T5_ post3
T3_ post1
T4_ post2
T5_ post3
T4_ post2
T5_ post3
T5_ post3
0.1250
2.7500
3.8750
4.0000
2.6250
3.7500
3.8750
1.1250
1.2500
0.1250
0.6447
0.6447
0.6447
0.6447
0.6447
0.6447
0.6447
0.6447
0.6447
0.6447
Bonferroni
Bonferroni
Bonferroni
Bonferroni
Bonferroni
Bonferroni
Bonferroni
Bonferroni
Bonferroni
Bonferroni
1.0000
0.0021
<
.0001
.0001
0.0003
<
<
.0001
0.0035
<
.0001
<.0001
0.0919
0.0627
0.8477
.0001
<
.0001
0.9195
0.6265
1.0000
Figure 10.30
Output of the
Multiple Comparisons
procedure.
For designs involving a repeated measure,
SAS Enterprise Guide
dis-
plays the Bonferroni corrected probabilities in the final column labeled
Adj P
. These values are somewhat different from those produced by SPSS.
To calculate the Bonferroni adjusted probabilities,
SAS Enterprise Guide
multiplies the uncorrected probabilities by the number of paired mean
comparisons. This is a very conservative approach to reducing the fam-
ilywise error rate. When the result of this multiplication yields a value
greater than 1,
SAS Enterprise Guide
displays a value of 1.0000 in the
Adj
P
column.
In the present study, we have five conditions and a total of ten possi-
ble pairwise comparisons. Thus, for example, the uncorrected probability
associated with the mean difference between
post1
and
post3
is 0.0627
(9th row in Figure 10.30) and the Bonferroni corrected adjusted proba-
bility is 0.6265 (because SAS keeps more decimal places than it typically
displays, simply multiplying the tabled values will lead to an inexact result).
SPSS does not have a post-ANOVA procedure in which we can select
“all pairwise comparisons.” The number of paired comparisons SPSS
assumesarebeingmadeatanyonetimearegenerallyfewerthanthe
number presumed by SAS, especially, as we will see in the remaining
chapters, when we perform simple effects analyses to explicate interaction
effects. For these reasons, SPSS will almost always produce Bonferroni
adjusted probabilities that are different (and less conservative) than those
obtained from
SAS Enterprise Guide
. One way to offset the extreme con-
servatism of SAS is use a different multiplier to compute the Bonferroni
correction if the number of comparisons you intend to make is fewer than
the total number of such comparisons displayed by SAS. In the present
study, a case could be made to compare each of the posttests to the final
pretest score for a total of three pairwise comparisons. Under this circum-
stance it would be appropriate to multiply the uncorrected probability
by 3 (rather than 10) to obtain the Bonferroni corrected probabilities for
those particular comparisons.
