Lecture 29: Analysis of Dental Pain Experiment
Dental Pain Experiment
JMP Data Table
is the overall population mean
is the effect of Drug i
is the effect of Acupuncture j
is the interaction effect
is the block effect
is random error
Block
Drug
Acupuncture
1
Codeine
Active
1.2
1
Codeine
Inactive
0.5
1
Placebo
Active
0.6
1
Placebo
Inactive
0.0
8
8
Placebo
Placebo
Active
Inactive
1.6
1.2
1
Relief
2
Important
Fit Model
Y: Relief
Construct Model Effects
Be sure that Block, Drug and
Acupuncture are all
Drug
Acupuncture
Drug*Acupuncture
Block
Data Type: Character
Modeling Type: Nominal
Otherwise JMP will do the
incorrect analysis.
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Complete ANOVA
Response Relief
Analysis of Variance
Source
Model
Error
C. Total
DF
10
21
31
Sum of
Squares Mean Square
F Ratio
1.13350 78.3654
11.335000
0.01446 Prob > F
0.303750
11.638750
<.0001*
Effect Tests
Source
Nparm
Drug
1
1
Acupuncture
1
Drug*Acupuncture
7
Block
DF
1
1
1
7
Sum of
F Ratio Prob > F
Squares Mean Square
2.3112500
2.311250 159.7901 <.0001*
3.3800000
3.380000 233.6790 <.0001*
0.0450000
3.1111 0.0923
0.045000
5.5987500
0.799821 55.2963 <.0001*
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Source
Drug
Acupuncture
Drug*Acu
Block
Error
C. Total
df
SS
1 2.31125
1 3.38000
1 0.04500
7 5.59875
21 0.30375
31 11.63875
MS
F Prob>F
2.31125 159.79 <0.0001
3.38000 233.68 <0.0001
0.04500
3.11 0.0923
0.79982
0.01446
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Lecture 29: Analysis of Dental Pain Experiment
Treatment Effects
SS Treatments
SSModel – SSBlock
11.335 – 5.59875 = 5.73625
10 – 7 = 3 df
JMP does not automatically
give you a test for treatment
effects.
You can find the SS for
treatments.
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SS Treatments
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Test for Treatment Effects
MSTreatment = 5.73625/3
=1.19208
F = 1.19208/0.01446 =132.23
P-value < 0.0001
The small P-value indicates that
there are some statistically
significant treatment effects.
SSDrug + SSAcupuncture +
SSDrug*Acupuncture
2.31125 + 3.38 + 0.045 =
5.73625
1 + 1 + 1 = 3 df
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Test for Drug Effects
Comment
F = 159.79, P-value < 0.0001
The small P-value indicates
that there are some statistically
significant Drug effects.
Because there are only 2 levels
of Drug, Codeine produces a
significantly higher average
pain relief (1.425) that Placebo
(0.8875).
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Lecture 29: Analysis of Dental Pain Experiment
Test for Acupuncture Effects
Comment
F = 233.68, P-value < 0.0001
The small P-value indicates
that there are some statistically
significant Acupuncture
effects.
Because there are only 2 levels
of Acupuncture, Active sites
produce a significantly higher
average pain relief (1.48125)
that Placebo (0.83175).
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Test for Interaction Effects
F = 3.11, P-value = 0.0923
The P-value is not small (>
0.05). This indicates that there
are no statistically significant
interaction effects.
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Recommendation
The effect of Drug is about the same
when Acupuncture is at Active or Inactive
sites. This is indicative of no statistically
significant interaction effects.
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Note
Based on the analysis of
factors and interaction, a
combination of Codeine and
acupuncture at Active sites
will give the highest average
pain relief.
If the interaction was
statistically significant then
you can’t rely on the optimal
level of each factor to give you
the overall optimal response.
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Lecture 29: Analysis of Dental Pain Experiment
Statistical Significance?
Multiple comparisons of
treatment (combination of
Drug and Acupuncture) means
is needed to confirm that the
recommendation is the best
treatment.
Tukey HSD
2
2.78733 0.01446
2
8
HSD = 2.78733(0.06013) = 0.1676
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Multiple Comparisons
Treatment
Codeine, Active
Placebo, Active
Codeine, Inactive
Placebo, Inactive
Comment
Mean
1.7875 A
1.1750
B
1.0625
B
0.6000
C
Treatments not connected by the same
letter are significantly different.
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Codeine and Active
acupuncture sites provides the
best treatment.
Placebo and Inactive
acupuncture sites provides the
worst treatment.
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Comment
Comment
There is no statistically
significant difference
between the average pain
relief from Codeine alone or
acupuncture at Active sites,
This provides oral surgeons
an option to prescribe either
drugs or acupuncture alone
as they give the same
average pain relief.
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