factorial design examples. a 2x3 example l study of the effect of different treatment combinations...
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Factorial Design ExamplesFactorial Design Examples
A 2x3 ExampleA 2x3 Example
Study of the effect of different treatment Study of the effect of different treatment combinations for cocaine abusecombinations for cocaine abuse
Dependent measure is severity of Dependent measure is severity of illness (ranges from 1 to 10) rated by illness (ranges from 1 to 10) rated by treatment stafftreatment staff
A 2x3 ExampleA 2x3 Example
Factor 1: TreatmentFactor 1: Treatment– PsychotherapyPsychotherapy– Behavior modificationBehavior modification
Factor 2: SettingFactor 2: Setting– InpatientInpatient– Day treatmentDay treatment– OutpatientOutpatient
A 2x3 ExampleA 2x3 Example
2
4
6
8
10
In
Da
y
Ou
t
psy
bmd
5 7
5 7
7
7
5 7
In Day
Psych
Behmod
Setting
Tre
atm
ent
Main Effectof Setting
2
4
6
8
10
ps
y
bm
d
In
Day
Out
9
9
9
Out
A 2x3 ExampleA 2x3 Example
2345678
In
Da
y
Ou
t
psy
bmd
5 5
7 7
5
7
6 6
In Day
Psych
Behmod
Setting
Tre
atm
ent
Main Effectof Treatment
2345678
ps
y
bm
d
In
Day
Out
5
7
6
Out
A 2x3 ExampleA 2x3 Example
2345678
In
Da
y
Ou
t
psy
bmd
5 6
7 6
6
6
6 6
In Day
Psych
Behmod
Setting
Tre
atm
ent
InteractionEffect
2345678
ps
y
bm
d
In
Day
Out
7
5
6
Out
A 2x3 ExampleA 2x3 Example
2
4
6
8
10
In
Da
y
Ou
t
psy
bmd
5 7
7 8
6
7
6 7.5
In Day
Psych
Behmod
Setting
Tre
atm
ent
InteractionEffect
2
4
6
8
10
ps
y
bm
d
In
Day
Out
6
6
6
Out
A Three Factor ExampleA Three Factor Example
Add the factor of medication dosage to Add the factor of medication dosage to the previous example.the previous example.
Dependent measure is also severity of Dependent measure is also severity of illness (ranges from 1 to 10) rated by illness (ranges from 1 to 10) rated by treatment staff.treatment staff.
A Three Factor ExampleA Three Factor Example
Factor 1: DosageFactor 1: Dosage 100 mg.100 mg. 300 mg.300 mg.
Factor 2: TreatmentFactor 2: Treatment PsychotherapyPsychotherapy Behavior modificationBehavior modification
Factor 3: SettingFactor 3: Setting InpatientInpatient Day treatmentDay treatment OutpatientOutpatient
A Three Factor ExampleA Three Factor Example
5 7
7 8
6
7
6 7.5
In Day
Psych
Behmod
Setting
Tre
atm
ent
6
6
6
Out
3 5
5 6
4
5
4 5.5
In Day
Psych
Behmod
Setting
Tre
atm
ent
4
4
4
Out
100 mg.
300 mg.
A Three Factor ExampleA Three Factor Example
Illustrates a 2x2x3 factorial design (12 Illustrates a 2x2x3 factorial design (12 treatment groups).treatment groups).
For each outcome you could have a For each outcome you could have a multitude of graphs.multitude of graphs.
There are three main effects -- one for There are three main effects -- one for each factor.each factor.
Can you tell what effects exist?Can you tell what effects exist?
Incomplete Factorial DesignIncomplete Factorial Design
Factors and levels are not fully crossed.Factors and levels are not fully crossed. You could do this for efficiency. (3+ You could do this for efficiency. (3+
factors means too many groups to be factors means too many groups to be feasible.)feasible.)
You could do this to include a single no-You could do this to include a single no-treatment (or placebo) control group.treatment (or placebo) control group.
Incomplete Factorial DesignIncomplete Factorial Design
5 7
7 8
6
7
6 7.5
In Day
Psych
Behmod
Setting
Tre
atm
ent
6
6
6
Out
9No-treatment control group