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Experimental Design & Analysis

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

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  1. Experimental Design & Analysis Three-Factor Experiments March 6, 2007 DOCTORAL SEMINAR, SPRING SEMESTER 2007

  2. 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

  3. Three-Factor Analysis 2x2x2 factorial design

  4. 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

  5. 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)

  6. Three-Factor Analysis • Sums of squares SST = SSA + SSB + SSC +SSAxB + SSAxC + SSBxC + SSAxBxC + SSS/ABC

  7. 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

  8. What’s the Story? Low involvement High involvement Impact of ad Impact of ad Celebrity Celebrity Unknown Unknown Strong Weak Strong Weak

  9. What’s the Story? Future Past Evaluation Evaluation Swiss Swiss Polish Polish Unfavorable Favorable Unfavorable Favorable

  10. 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

  11. 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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