Wednesday, December 1

Factorial Design ANOVA

The factorial design is used to study the relationship of two or more independent variables (called factors) to a dependent variable, where each factor has two or more levels. - p. 333

The factorial design is used to study the relationship of two or more independent variables (called factors) to a dependent variable, where each factor has two or more levels.

In this design, you can evaluate the main effects of each factor independently (essentially equivalent to doing one-way ANOVA’s for each of the factors independently), but you are also able to evaluate how the two (or more factors) interact.

Examples of Interaction Effects

• Two drugs in combination may have a negative effect – aspirin is not effective for angina if combined with ibuprofen.

• An educational intervention program may be more effective for one group (boys) than for another (girls).

0.5 1.0 1.5 2.0 2.5 3.0 3.5SES

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80RDG

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RACE

0.5 1.0 1.5 2.0 2.5 3.0 3.5SES

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80MATH

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RACE

TOTAL VARIATION

Variation within groups (error)

Variation between groups

Variationfrom Factor 1

Variationfrom Factor 2

Variation from Factor 1 x 2 interaction

Partitioning variation in a factorial design.

1.A Compute SST

B. Compute SSB

C. Subtract SSB from SST to obtain SSW (error) D. Compute SS1

E. Compute SS2

F. Compute SS1x2 by subtracting SS1 and SS2 from SSB

2. Convert SS to MS by dividing SS by the appropriate d.f.

3. Test MS1,MS2 and MS1x2 using F ratio.

More advanced ANOVA topics

• N-way ANOVA

• Repeated Measures designs

• Mixed models

• Contrasts