Lecture 30: More on Factorial Crossing
Treatments and Factors
Example 1
Factor A: two levels
Factor B: two levels
The four treatment
combinations are replicated 5
times.
Completely randomized
design.
You can’t tell if factors are
statistically significant even
if treatments are statistically
significant without doing
the appropriate tests.
1
2
Treatments
Factors
There are statistically significant
treatment effects.
F = 4.2244, P-value = 0.0222.
Treatment A1,B2 has the highest
mean and it is statistically
different from all other
treatments.
No factor nor interaction is
statistically significant. F
values of 4.224, P-values of
0.0565.
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Example 2
4
Treatments
Factor A: two levels
Factor B: two levels
The four treatment
combinations are replicated 5
times.
Completely randomized
design.
There are no statistically
significant treatment effects.
F = 2.1331, P-value =
0.1361.
5
6
1
Lecture 30: More on Factorial Crossing
Factors
The interaction between
Factors A and B is
statistically significant. F
value of 6.3992, P-values of
0.0223.
7
Handout
The effect of Factor B is positive for
Level A1 but negative for Level A2.
This is indicative of an interaction
between the two factors.
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Parameter Estimates
JMP produces Parameter
Estimates as part of its Fit
Model output.
These are related to
estimated effects.
See the handout on the
course web site for the data
and JMP output for both
examples.
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Dental Pain Relief
10
Estimated Drug Effects
Parameter Estimates
Term
Estimate
Intercept
1.15625
Drug[Codeine]
0.26875
Acupuncture[Active]
0.32500
Drug[Codeine]*Acupuncture[Active]
0.0375
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Level
Codeine
Placebo
Mean Estimated Effect
1.4250 1.4250 – 1.15625 = +0.26875
0.8875 0.8875 – 1.15625 = –0.26875
The parameter estimate for Drug[Codeine]
is the estimated drug effect for Codeine.
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2
Lecture 30: More on Factorial Crossing
Estimated Acupuncture Effects
Level
Active
Inactive
Estimated Interaction Effects
Active
+0.0375
–0.0375
Codeine
Placebo
Mean Estimated Effect
1.48125 1.48125 – 1.15625 = +0.325
0.83125 0.83125 – 1.15625 = –0.325
The parameter estimate for Acupuncture[Active]
is the estimated acupuncture effect for Active.
Inactive
–0.0375
+0.0375
The parameter estimate for
Drug[Codeine]*Acupuncture[Active]
is the estimated interaction effect for
Codeine*Active.
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14
Model
Estimated Treatment Effects
JMP does not provide a
parameter estimate that gives
the estimated treatment effects
but you can calculate these
from the parameter estimates
given.
15
Parameter Estimates
16
Estimated Treatment Effects
Drug[Codeine] +
Acupuncture[Active] +
Drug[Codeine]*Acupuncture
[Active] = 0.26875 + 0.325 +
0.0375 = 0.63125
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Level
Codeine,Active
Codeine,Inactive
Placebo,Active
Placebo,Inactive
Mean
1.7875
1.0625
1.1750
0.6000
Estimated Effect
1.7875 – 1.15625 = +0.63125
1.0625 – 1.15625 = –0.09375
1.1750 – 1.15625 = +0.01875
0.6000 – 1.15625 = –0.55625
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