Treatment by Subject Design

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Treatment by Subject Design
Structural Approach
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Simple Model
Source E(MS) Subject Condition (T) Error
This is not the model that we use!
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Complex Model
Source E(MS) Subject Condition (T) Error
This IS the model that we use!
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Treatment by Subject Design
Treatment
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Correcting for Dependence
Treatment
Equate Subject Means
Treatment
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Treatment
Remove GM effect
Treatment
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Treatment by Subject Design
Treatment
Treatments are no longer independent. We must
remove (partial out) the dependence.
Treatment
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Remove Subject Effects
Treatment
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Remove Treatment Effects
Treatment
SSTreat ?
SSbs ?
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TxS or Repeated Measures
df
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Repeated Measures Design
Partitioning SSTotal
SSTotal
SSbs
SSws
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SSws
sum across subjects in the jth condition
continued
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SSws (continued)
now, sum across treatments or conditions.
SSws

SSTreat SSres
(k-1)df (n-1)(k-1)df
n(k-1)df

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SSws df
The mean for each subject is fixed. With 3
treatments we have 2df within each subject. We
have 5 subjects.
Thus, 2 x 5 10df
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SSTreat df
Treatment
The GM is fixed. With 3 treatments only two are
free to vary. Thus, 3 1 2df
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SSres df
Treatment
The mean for each subject is fixed. Thus, (k-1)
The mean for each treatment is fixed. Thus,
(n-1)
The GM is fixed. But nothing is lost since all
treatment means are fixed already. Thus,
(k-1)(n-1)
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Treatment by Subject Design
SSws
SSbs
SSTreat
SSres(error)
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Treatments

SSTotal

227.6

SSbs

177.6

SSTreat

43.2
SS(res)error


6.8
SSws SSTotal SSbs or SSTreat SSerror