Lecture 32: Solitary Confinement Experiment
Solitary Confinement
Experiment
Solitary Confinement
Experiment
Response: Frequency of brain
waves.
Conditions:
12 to 36 Hz – alert.
8 to 12 Hz – relaxed inactivity.
Below 8 Hz – abnormal for
someone who is awake.
Solitary Confinement – Yes,
No.
Time – 1 day, 4 days, 7 days.
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Solitary Confinement
Experiment
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Solitary Confinement
Experiment
Treatment Combinations;
Experimental Material
There are 6 treatment
combinations: Yes,1day;
Yes,4days; Yes,7days;
No,1day; No,4days; and
No,7days.
20 prisoners at a maximum
security penitentiary.
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Completely Randomized
Completely Randomized
If we were to use a completely
randomized design we could
use only 18 prisoners (has to
be a multiple of the number of
treatment combinations, 6).
Each of the 6 treatment
combinations would be
assigned, at random, to 3
prisoners.
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Lecture 32: Solitary Confinement Experiment
Analysis of Variance
Source
Solitary
Time
Solitary*Time
Error
C. Total
Random Error
df
1
2
2
12
17
Differences among prisoners
treated the same will
contribute to random error.
For example, different
prisoners may have different
natural brain wave
frequencies.
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Block Design
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Comment
We could sort on natural brain wave
frequencies to make blocks of size 6.
Prisoners within a block are
more similar in terms of
natural brain wave
frequencies but will not be
exactly the same.
 Block 1: 6 prisoners with the highest
frequencies.
 Block 2: 6 prisoners with the next
highest frequencies.
 Block 3: 6 prisoners with the lowest
frequencies.
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Randomization
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Analysis of Variance
Randomly assign the 6
treatment combinations to
the 6 prisoners within each
block.
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Source
Solitary
Time
Solitary*Time
Block
Error
C. Total
df
1
2
2
2
10
17
12
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Lecture 32: Solitary Confinement Experiment
Error
Alternative Blocking
The sum of squares error in a
block design is the interaction
between treatments and blocks
(df = 5*2 = 10).
This is the inconsistency of
treatment effect across blocks.
Reuse prisoners so that each
prisoner experiences all 6
treatments.
The order of the treatments is
randomized for each prisoner.
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Alternative Blocking
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Analysis of Variance
Advantages: Can use all 20
prisoners. Reusing forms the
most uniform (homogeneous)
blocks.
Disadvantages: More time for
the experiment (24 days).
Difficult to run. What to do with
treatment carry over effects?
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Source
Solitary
Time
Solitary*Time
Prisoner
Error
C. Total
df
1
2
2
19
95
119
Error
Repeated Measures
The sum of squares error in a
block design is the interaction
between treatments and
prisoners (df = 5*19 = 95).
This is the inconsistency of
treatment effect across
prisoners.
Whole plot/Between subject
factor: Solitary – Yes, No.
Sub plot/Within subject
factor: Time – 1, 4 and 7
days.
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Lecture 32: Solitary Confinement Experiment
Completely Randomized
Comment
Randomly assign solitary
confinement to 10 prisoners
and no solitary confinement
to the other 10 prisoners.
If we didn’t have the second
factor of time, the analysis
would have two sources of
variation; solitary and error.
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Random Error
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Analysis of Variance
The sum of squares for error
comes from differences among
prisoners treated the same.
Solitary – 10 prisoners – 9 df
No solitary – 10 prisoners – 9 df
Source
Solitary
Error
C. Total
df
1
18
19
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Analysis of Variance
Source
Solitary
Prisoners[Solitary]
C. Total
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Block Design
df
1
18
19
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Reuse the prisoners by
measuring their brain waves
on days 1, 4 and 7.
Repeatedly measure their
brain waves.
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Lecture 32: Solitary Confinement Experiment
Analysis of Variance
Source
Solitary
Prisoners[Solitary]
Time
Solitary*Time
Error
C. Total
df
1
18
2
2
36
59
Error
The sum of squares error in a
block design is the interaction
between time variable and
prisoners (df = 2*18 = 36).
This is the inconsistency of the
effect of time across prisoners.
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Comment
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Comment
Variation among prisoners in
the same confinement does not
come into play when
evaluating the effects of time
or the interaction effects of
Solitary*Time.
Variation among prisoners
in the same confinement
(solitary or no solitary) is
accounted for separately in
the analysis of variance.
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Comment
Comment
When evaluating the effects of
solitary confinement (Yes or
No) the variation among
prisoners in the same
confinement is the error term
and will probably be fairly
large.
It will be harder to see
differences in average brain
wave frequencies due to
confinement than it will to see
differences due to time or the
interaction between Solitary
and Time.
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