1. Factorial Design Examples

2. A 2x3 Example
Study of the effect of different treatment combinations for cocaine abuse
Dependent measure is severity of illness (ranges from 1 to 10) rated by treatment staff

3. A 2x3 Example Factor 1: Treatment Factor 2: Setting Psychotherapy
Behavior modification
Factor 2: Setting
Inpatient
Day treatment
Outpatient

4. A 2x3 Example Main Effect of Setting Setting 5 7 9 7 Treatment 5 7 9 7
Day
Out
Main Effect
of Setting 5 7 9 7
Psych
Treatment 5 7 9 7
Behmod 5 7 9

5. A 2x3 Example Main Effect of Treatment Setting 5 5 5 5 Treatment 7 7 7
Day
Out
Main Effect
of Treatment 5 5 5 5
Psych
Treatment 7 7 7 7
Behmod 6 6 6

6. A 2x3 Example Interaction Effect Setting 5 6 7 6 Treatment 7 6 5 6 6 6
Day
Out
Interaction
Effect 5 6 7 6
Psych
Treatment 7 6 5 6
Behmod 6 6 6

7. A 2x3 Example Interaction Effect Setting 5 7 6 6 Treatment 7 8 6 7 6
Day
Out
Interaction
Effect 5 7 6 6
Psych
Treatment 7 8 6 7
Behmod 6
7.5 6

8. A Three Factor Example
Add the factor of medication dosage to the previous example.
Dependent measure is also severity of illness (ranges from 1 to 10) rated by treatment staff.

9. A Three Factor Example Factor 1: Dosage Factor 2: Treatment
100 mg.
300 mg.
Factor 2: Treatment
Psychotherapy
Behavior modification
Factor 3: Setting
Inpatient
Day treatment
Outpatient

10. A Three Factor Example 100 mg. 300 mg. Setting 5 7 6 6 Treatment 7 8 6
Day
Out 5 7 6 6
Psych
100 mg.
Treatment 7 8 6 7
Behmod 6
7.5 6
Setting In
Day
Out 3 5 4 4
Psych
300 mg.
Treatment 5 6 4 5
Behmod 4
5.5 4

11. A Three Factor Example
Illustrates a 2x2x3 factorial design (12 treatment groups).
For each outcome you could have a multitude of graphs.
There are three main effects -- one for each factor.
Can you tell what effects exist?

12. Incomplete Factorial Design
Factors and levels are not fully crossed.
You could do this for efficiency. (3+ factors means too many groups to be feasible.)
You could do this to include a single no-treatment (or placebo) control group.

13. Incomplete Factorial Design
Setting In
Day
Out 5 7 6 6
Psych
Treatment 7 8 6 7
Behmod 6
7.5 6 9
No-treatment control group