Lecture 36: Three Factors - CRD
Experiments
Experiments
The rest of the semester
will look at different
experiments using different
combinations of factorial
crossing and designs.
Factorial Crossing
Design
CRD, RCBD, RLSq, Split
Plot/Repeated Measures.
1
Agoraphobia
2
Agoraphobia
Factor 1: Drug (4 levels)
Factor 2: Psychotherapy (3
levels)
Factor 3: Depression (2
levels)
Response: Severity of
agoraphobia (fear of public
places).
A higher score indicates
more severe symptoms.
3
4
Comment
Comment
Drug and Psychotherapy are
experimental factors that
can be assigned at random
to patients suffering from
agoraphobia.
Depression is an
observational factor that is
associated with a patient
suffering from agoraphobia.
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1
Lecture 36: Three Factors - CRD
Treatments
Randomization
 Select three depressed patients at
random and assign one of the Drug,
Psychotherapy combinations.
 Select three non-depressed patients at
random and assign one of the Drug,
Psychotherapy combinations.
 Do this until all 12 combinations are
assigned to 3 depressed and 3 nondepressed patients.
There are 12 combinations of
Drug and Psychotherapy that can
be assigned to depressed and
non-depressed patients.
There are 24 combinations of
Depression, Drug and
Psychotherapy.
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JMP Table
Drug
Prozac
Prozac
Prozac
Elavil
Therapy
Psychodynamic
Psychodynamic
Psychodynamic
Psychodynamic
Placebo Group
JMP – Fit Model
Y: Severity
Construct Model Effects
Depressed Severity
No
11
No
12
No
7
No
13
Yes
8
Highlight Drug, Therapy,
Depression
Macros – Full Factorial
13
9
10
Response Severity
Construct Model Effects
Drug
Therapy
Drug*Therapy
Depression
Drug*Depression
Therapy*Depression
Drug*Therapy*Depression
Summary of Fit
RSquare
0.88434
RSquare Adj
0.82892
Root Mean Square Error
1.658312
Mean of Response
13.30556
Observations (or Sum Wgts)
72
Analysis of Variance
Source
Model
Error
C. Total
DF
23
48
71
Sum of
F Ratio
Squares Mean Square
1009.2778
43.8816 15.9570
132.0000
2.7500 Prob > F
1141.2778
<.0001*
Effect Tests
Source
Nparm
Drug
3
Therapy
2
Drug*Therapy
6
Depression
1
Drug*Depression
3
Therapy*Depression
2
Drug*Therapy*Depression
6
11
DF
3
2
6
1
3
2
6
Sum of
Squares
486.72222
33.36111
385.52778
40.50000
20.94444
31.08333
11.13889
F Ratio Prob > F
<.0001*
58.9966
0.0045*
6.0657
<.0001*
23.3653
0.0004*
14.7273
0.0675
2.5387
0.0063*
5.6515
0.6703
0.6751
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2
Lecture 36: Three Factors - CRD
Drug Effect
Drug Effect
2
F = 58.9966, P-value <
0.0001, statistically
significant because of the
small P-value.
2.66137 2.75
2
18
HSD = 2.66137(0.55277) = 1.47
13
Drug Effect
Drug
Placebo
Xanax
Elavil
Prozac
Therapy Effect
Mean
16.333 A
15.278 A
11.667
B
9.944
F = 6/0657, P-value =
0.0045, statistically
significant because of the
small P-value.
C
Drugs not connected by the same
letter are significantly different
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Therapy Effect
16
Therapy Effect
Therapy
Psychodynamic
Group
Cog/Beh
2
L
14
2.01063 2.75
Mean
14.125 A
13.333 A
12.458
B
B
Therapies not connected by the same
letter are significantly different
LSD = 2.01063(0.47871) = 0.96
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18
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Lecture 36: Three Factors - CRD
Depression Effect
Depression Effect
Depression
No
Yes
F = 14.7273, P-value =
0.0004, statistically
significant because of the
small P-value.
Mean
14.056 A
12.556
B
Because the F statistic indicated a
statistically significant difference,
the mean for no depression is significantly
different from the mean with depression.
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20
Main (Factor) Effects
Drug*Therapy
So far we have only looked
at the effects of individual
factors.
What about interactions?
F = 23.3653, P-value <
0.0001. The small P-value
indicates a statistically
significant interaction
between Drug and Therapy.
21
22
25
Elavil
Placebo
Prozac
Xanax
Severity LS Means
20
Interpretation
15
Prozac has about the same
effect for each type of therapy.
Elavil has about the same
effect (not as good as Prozac)
for each type of therapy.
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5
Cog/Beh
Group
Psychodynamic
Therapy
23
24
4
Lecture 36: Three Factors - CRD
Interpretation
Interpretation
The effect of Xanax is
better with Cog/Beh therapy
and not so good with Group
or Psychodynamic therapy.
The effect of Placebo is not
very good for Cog/Beh or
Psychodynamic but it is
effective with Group
therapy.
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26
Therapy*Depression
25
Cog/Beh
Group
Psychodynamic
20
Severity LS Means
F = 5.6515, P-value < 0.0063.
The small P-value indicates a
statistically significant
interaction between Therapy
and Depression.
15
10
5
No
Yes
Depression
27
Interpretation
28
Interaction Effects
There is no statistically
significant interaction for
For depressed patients all
therapies give similar results.
For non-depressed patients,
Cog/Beh has lowest average
severity followed by Group
and Psychodynamic.
Drug*Depression: F = 2.53878,
P-value = 0.0675.
Drug*Therapy*Depression: F
= 0.6751, P-value = 0.6703.
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Lecture 36: Three Factors - CRD
Recommendation?
Different Analysis?
It is hard to make a
recommendation based on
the factors and interactions
especially because of the
interaction terms.
Analyze the data from the
36 depressed patients
separately from the data
from the 36 non-depressed
patients.
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Not Depressed
Source
Not Depressed
df
Sum of
Squares
Mean
Square
F Ratio
Prob>F
Drug
3
334.778
111.5926
40.1733
<0.0001
Therapy
Drug*Therapy
2
6
64.056
176.389
32.0278
29.3981
11.5300
10.5833
0.0003
<0.0001
2.7778
Error
24
66.667
C. Total
35
641.889
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Elavil and Prozac are
equally effective and
significantly better than
Placebo or Xanax.
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Not Depressed
34
Not Depressed
Cog/Beh is significantly
better than Group or
Psychodynamic therapies.
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36
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Lecture 36: Three Factors - CRD
Recommendation
Depressed
For patients who are not
depressed.
Source
You should get reasonably good
results using either Prozac or
Elavil and any of the Therapies
Xanax and Cog/Beh or Placebo
and Group are not much different.
df
Sum of
Squares
Mean
Square
F Ratio
Prob>F
Drug
3
172.889
57.6296
21.1701
<0.0001
Therapy
Drug*Therapy
2
6
0.389
220.278
0.1944
36.7130
0.0714
13.4864
0.9313
<0.0001
2.7222
Error
24
65.333
C. Total
35
458.889
37
Depressed
38
Depressed
Elavil and Prozac are
equally effective and
significantly better than
Placebo or Xanax.
There is no statistically
significant effect of
Therapy.
39
Depressed
40
Recommendation
For patients who are depressed.
You should get reasonably good
results using Prozac and any of the
Therapies.
Xanax and Cog/Beh or Elavil and
Psychodynamic are not much
different.
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