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Experimental Design & 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

Experimental Design & Analysis

Three-Factor Experiments

March 6, 2007

DOCTORAL SEMINAR, SPRING SEMESTER 2007


Three factor experiments
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

      • For large companies vs. small companies

      • For Americans vs. Europeans


Three factor analysis
Three-Factor Analysis

2x2x2 factorial design


Three factor analysis1
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 analysis2
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 analysis3
Three-Factor Analysis

  • Sums of squares

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


Three factor analysis4

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

Collapse 3-way design into 2-way design for analysis and interpretation

Three-Factor Analysis


What s the story
What’s the Story?

Low involvement

High involvement

Impact

of ad

Impact

of ad

Celebrity

Celebrity

Unknown

Unknown

Strong

Weak

Strong

Weak


What s the story1
What’s the Story?

Future

Past

Evaluation

Evaluation

Swiss

Swiss

Polish

Polish

Unfavorable

Favorable

Unfavorable

Favorable


What s the story2
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 story3
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


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