Experimental Design &amp; Analysis

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# Experimental Design & Analysis - PowerPoint PPT Presentation

Experimental Design &amp; Analysis. Three-Factor Experiments March 6, 2007. Three-Factor Experiments. Advantage of 3-factor experiment is that it allows greater understanding of theoretical relationships 2-way interaction may be further qualified For men vs. women For children vs. adults

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### Experimental Design & Analysis

Three-Factor Experiments

March 6, 2007

DOCTORAL SEMINAR, SPRING SEMESTER 2007

Three-Factor Experiments
• Advantage of 3-factor experiment is that it allows greater understanding of theoretical relationships
• 2-way interaction may be further qualified
• For men vs. women
• For large companies vs. small companies
• For Americans vs. Europeans
Three-Factor Analysis

2x2x2 factorial design

Three-Factor Analysis
• Examining the model for sources of variance when A, B and C are independent variables
• A
• B
• C
• AxB, BxC, AxC
• AxBxC
• S/AxBxC

Main effects

Two-wayinteractions

Three-way interaction

Three-Factor Analysis
• Sources of variance when A, B and C are independent variables
• A
• B
• C
• AxB, AxC, BxC
• AxBxC
• S/AxBxC

Yijk = μ + αi + βj + γk + (αβ)ij + (αγ)ik + (βγ)jk + (αβγ)ijk+ εijk

Error term, also

known as S/AxBxC,

or randomness

Interaction

effect of α, γ

Interaction

effect of β, γ

Interaction

effect of α, β

Interaction effect of

α,β, γ (effect left in data

after subtracting off

lower-order effects)

Three-Factor Analysis
• Sums of squares

SST = SSA + SSB + SSC +SSAxB + SSAxC + SSBxC + SSAxBxC + SSS/ABC

Is 3-way interaction significant? Yes

Examine simple interactions (two 2-way interactions, e.g. interaction of AxB at C1 and interaction of AxB at C2)

If simple interactions are significant, examine contrasts

Is 3-way interaction significant? No

Three-Factor Analysis
What’s the Story?

Low involvement

High involvement

Impact

Impact

Celebrity

Celebrity

Unknown

Unknown

Strong

Weak

Strong

Weak

What’s the Story?

Future

Past

Evaluation

Evaluation

Swiss

Swiss

Polish

Polish

Unfavorable

Favorable

Unfavorable

Favorable

What’s the Story?

No distraction

Distraction

Evaluation

Evaluation

Not poor

in vitamin E

Not poor

in vitamin E

Not rich

in vitamin E

Not rich

in vitamin E

Personally

relevant

Personally

irrelevant

Personally

relevant

Personally

irrelevant

What’s the Story?

Promotion prime

Prevention prime

Consumer

ranking

Consumer

ranking

Core product

benefits

Core product

benefits

Core product

costs

Core product

costs

Poor

peripherals

Good

peripherals

Poor

peripherals

Good

peripherals