Lecture 34: More Analysis – Solitary Confinement
Fit Model
JMP Output: ANOVA
Y: Frequency
Construct Model Effects
Source
Model
Error
C. Total
Solitary
Prisoner[Solitary]
Day
Solitary*Day
df Sum of Squares
23
2375.6
36
102.0
59
2477.6
1
JMP Output: Effect Tests
Source
Solitary
Prisoner[Solitary]
Day
Solitary*Day
df Sum of Squares
1
248.0667
18
1610.2000
2
256.9000
2
260.4333
2
Comment
JMP calculates all the sums of
squares and degrees of
freedom correctly, however,
we have not told JMP that a
split plot design was used to
collect the data and so some of
the F tests are incorrect.
3
Analysis of Variance
Source
Solitary
Prisoner[Solitary]
Day
Solitary*Day
Error
C. Total
4
Effect of Solitary
df Sum of Squares Mean Square
1
248.0667
248.0667
18
1610.2000
89.4556
2
256.9000
128.4500
2
260.4333
130.2170
36
102.0000
2.8333
59
2477.6000
5
Because solitary confinement
condition (Yes, or No) is
assigned to prisoners completely
at random, the Prisoner[Solitary]
source of variation quantifies the
random error variation for
evaluating the effect of solitary
confinement.
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Lecture 34: More Analysis – Solitary Confinement
Effect of Solitary
JMP
The F statistics used to
evaluate the effect of solitary
confinement should be the
ratio of the mean square for
Solitary to the mean square for
Prisoner[Solitary].
To get JMP to do this you need
to tell JMP that the random error
for Solitary is quantified by
Prisoner[Solitary].
Highlight Prisoner[Solitary] in
the Construct Model Effects box
and go to Attributes – Random
Effect.
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8
JMP
Effect of Solitary
You will need to change the
Method from REML
(Recommended) to EMS
(Traditional) in the upper
right corner of the Fit
Model dialog box.
F = (248.067)/89.4556 =
2.7731, P-value = 0.1132.
The P-value is > 0.05, so there
is no statistically significant
difference between solitary
and no solitary.
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Comment
10
Effect of Day
The difference in means,
prisoners not in solitary have a
mean frequency that is 4 Hz
higher than those in solitary, is
not statistically significant
because the natural variation
among prisoners treated the
same is so large.
F = (128.45)/2.833 = 45.3353,
P-value < 0.0001.
The P-value is so small, there
are differences among some of
the day mean frequencies.
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Lecture 34: More Analysis – Solitary Confinement
Multiple Comparisons
∗
2.02809 2.833
Multiple Comparisons
Day
1
4
7
2
2
20
Mean
16.65
12.95
11.80
A
B
C
Days not connected by the same
letter are significantly different.
1.08Hz
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Linear Contrast
Linear Contrast
The levels for Day are equally
spaced numerical values.
Is there a linear relationship
between Day and average
frequency?
Day
Coeff
Mean
1
–1
16.65
4
0
12.95
7
–1
11.80
Contrast = –4.85
SSContrast=20(–4.85)2/2 = 235.225
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16
Linear Contrast
Quadratic Contrast
F = 235.225/2.833 = 83.03
P-value < 0.0001
The P-value is small. There is
a statistically significant linear
relationship between day and
average frequency.
F = 21.675/2.833 = 7.65
P-value = 0.0089
The P-value is less than 0.05.
There is a statistically
significant quadratic contrast.
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Lecture 34: More Analysis – Solitary Confinement
Comment
Interaction Effects
F = (130.217)/2.833 =
45.9588, P-value < 0.0001.
The small P-value indicates
that there is a statistically
significant interaction between
Solitary and Day.
As day increases, average
frequency decreases. The
decrease is faster at first and
not as fast as you approach
day 7.
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20
Interaction Effects
There is no effect of day when
prisoners are not in solitary
confinement.
For prisoners in solitary
confinement, as day increases,
average frequency decreases.
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Comment
Comment
The interaction effect is the
most important clue as to what
is happening.
There is a negative effect on
brain wave frequency the
longer one stays in solitary
confinement.
The decrease in average
frequency from day 1 to day
4 is greater than that from
day 4 to day 7.
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