Pretest/Posttest/Group
ANCOV
The Univariate Approach
Airport Search Data
•
•
•
•
Passengers at RDU in Sept., 2004
Race: 1 = Caucasian, 2 = Arab
Sex: 1 = Male, 2 = Female
Pre = Prior to 9/11, how many times
searched on 10 international flights.
• Post = same, but after 9/11.
Posttest Only Scores
• Independent t comparing the groups.
• Less powerful that other techniques
Mixed Factorial ANOVA
• Y = Time Race Time x Race
Tests of Within-Subjects Contrasts
Measure:MEASURE_1
Type III Sum
Source
PostPre of Squares
PostPre
Linear
288.364
PostPre * race Linear
76.364
Error(PostPre) Linear
180.491
df
Mean Square
1
288.364
F
84.676
Sig.
.000
1
76.364
22.424
.000
53
3.405
The interaction is of greatest importance, and it is significant
Simple Effects of Time, Arabs
Paired Samples Statisticsa
Mean
Pair 1
Std. Error
Mean
Std. Deviation
N
Post-9-11
Pre-9-11
Post-9-11 - Pre-9-11
7.67
21
3.512
.766
2.62
21
1.161
.253
Paired Differences
95% Confidence Interval
of the Difference
Sig. (2tailed)
Lower
Upper
t
df
3.397
6.698 6.379
20
.000
Caucasians
Paired Samples Statisticsa
Pair 1
Post-9-11
Pre-9-11
Post-9-11 - Pre-9-11
Mean
2.82
1.21
N
Std. Deviation
34
1.290
34
1.572
Std. Error
Mean
.221
.270
Paired Samples Testa
Paired Differences
95% Confidence Interval
of the Difference
Lower
Upper
t
df
1.016
2.219 5.473
33
Sig. (2tailed)
.000
Independent t on Difference Scores
• Diff = Post minus Pre
Group Statistics
race
Post Minus Pre Arab
Caucasian
N
21
34
Mean
Std. Deviation
5.0476
3.62596
1.6176
1.72354
Std. Error
Mean
.79125
.29558
Independent Samples Test
t-test for Equality of Means
Post Minus Pre
Equal variances assumed
t
4.735
df
Sig. (2-tailed)
53
.000
Equivalent to F test of Interaction
• t test on difference scores is absolutely
equivalent to F test of interaction
• t(53) = 4.735, p < .001
• Square that t: 4.735**2 = 22.42
• F(1, 53) = 22.42
• The t will always have the same p as does
the F.
Analysis of Covariance
• Post = Pre Group
Dependent Variable:Post-9-11
Type III Sum of
Squares
Source
Corrected Model
310.064a
Intercept
437.205
pre
5.563
race
214.378
Error
296.045
Total
1807.000
Corrected Total
606.109
df
2
1
1
1
52
55
54
Mean Square
155.032
437.205
5.563
214.378
5.693
F
27.231
76.795
.977
37.655
Sig.
.000
.000
.327
.000
Notice that the F for race is even larger than obtained
earlier for the interaction. The ANCOV is more powerful.
Least Squares Means
Race
Dependent Variable:Post-9-11
Race
Mean
Std.
Error
95% Confidence
Interval
Lower
Upper
Bound
Bound
Arab
7.469
.558
6.350
8.588
Caucasian
2.946
.427
2.088
3.803
The two groups differ significantly on posttest
scores after adjusting for the pretest scores.
Which Procedure Should I Use?
• Monte Carlo work has shown that the
ANCOV will give more power than will the
Time x Groups ANOVA.
• But you may still want to look at the
magnitude of the pre/post difference within
each group.