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Investigate the impact of different treatment combinations on cocaine abuse severity (rated 1-10). Psychotherapy and setting (inpatient, day treatment, outpatient) are the main factors evaluated. Add a third factor of medication dosage (100 mg, 300 mg). This provides insight into interaction effects and main effects of each factor. Incomplete factorial design may involve not fully crossing factors or including a no-treatment control group for efficiency.
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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
A 2x3 Example • Factor 1: Treatment • Psychotherapy • Behavior modification • Factor 2: Setting • Inpatient • Day treatment • Outpatient
A 2x3 Example Setting Main Effect of Setting In Day Out 5 7 9 7 Psych Treatment 5 7 9 7 Behmod 5 7 9
A 2x3 Example Setting Main Effect of Treatment In Day Out 5 5 5 5 Psych Treatment 7 7 7 7 Behmod 6 6 6
A 2x3 Example Setting Interaction Effect In Day Out 5 6 7 6 Psych Treatment 7 6 5 6 Behmod 6 6 6
A 2x3 Example Setting Interaction Effect In Day Out 5 7 6 6 Psych Treatment 7 8 6 7 Behmod 6 7.5 6
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.
A Three Factor Example • Factor 1: Dosage • 100 mg. • 300 mg. • Factor 2: Treatment • Psychotherapy • Behavior modification • Factor 3: Setting • Inpatient • Day treatment • Outpatient
A Three Factor Example Setting In 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
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?
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.
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