DOCTORAL SEMINAR, SPRING SEMESTER 2007 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 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-way interactions 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 Y ijk = μ + α i + β j + γ k + (αβ) ij + (αγ) ik + (βγ) jk + (αβγ) ijk + ε ijk Interaction effect of α, β Interaction effect of α, β, γ (effect left in data after subtracting off lower-order effects) Error term, also known as S/AxBxC, or randomness Interaction effect of α, γ Interaction effect of β, γ

Three-Factor Analysis Sums of squares SS T = SS A + SS B + SS C +SS AxB + SS AxC + SS BxC + SS AxBxC + SS S/ABC

Three-Factor Analysis Is 3-way interaction significant? Yes  Examine simple interactions (two 2-way interactions, e.g. interaction of AxB at C 1 and interaction of AxB at C 2 )  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

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

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

What’s the Story? Personally irrelevant Personally relevant Personally irrelevant Not poor in vitamin E Not rich in vitamin E Personally relevant Not poor in vitamin E Not rich in vitamin E No distractionDistraction Evaluation

What’s the Story? Good peripherals Poor peripherals Good peripherals Core product costs Core product benefits Poor peripherals Core product benefits Core product costs Promotion primePrevention prime Consumer ranking Consumer ranking