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Objectives

Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 13: Between-Subjects Factorial Designs. Objectives. Two-variable design GLM and two-variable design Advantages of 2-variable design Main effects Interactions Designing a two-variable study. Two-Variable Design.

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Objectives

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  1. Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 13: Between-Subjects Factorial Designs

  2. Objectives • Two-variable design • GLM and two-variable design • Advantages of 2-variable design • Main effects • Interactions • Designing a two-variable study

  3. Two-Variable Design • Relationship between two IV and a DV • How much does each IV influence DV? • How much do the IVs together influence DV?

  4. Figure 13.1

  5. GLM and Two-Variable Design • Single-variable, Xij = µ + αj + εij • Now, Xij = µ + αj + βk + αβjk + εijk

  6. Advantages of 2-Variable Design • Efficiency • Fewer people, more power to examine more questions simultaneously • See Table 13.1 • Can consider interaction of variables • Influence of variable combinations • Increased power • W-g variance < in one-group design

  7. A Bit More on Interactions • Pattern of results unexplainable by a single IV by itself • Compare Figure 13.2 with 13.3

  8. Figures 13.2 & 13.3

  9. Variables, Levels, Cells • Factorial design = study with independent groups for each possible combination of levels of the IV • e.g., A x B, 2 x 2, 3 x 4 • Can have more than 2 variables (A x B x C) • Here we consider A x B

  10. Example • From text, “Reaction to Product Endorsement” • DV = Willingness to buy • IV A = source credibility (high vs. low) • IV B = type of review (strong, ambiguous, and weak) • 2 x 3 factorial design (Figure 13.4) • Interaction of A x B

  11. Main Effects • Effect of one IV on the DV, holding the other IV constant • Special form of b-g variance • Two-factor design has two main effects • Fig. 13.8 and 13.9(a) = significant findings • Fig. 13.9(b) = nonsignificant findings

  12. Figure 13.8

  13. Figure 13.9

  14. More on Main Effects • Main effect = additive effect • Figure 13.10

  15. More on Interactions • Interaction = interplay between two variables • Figures 13.11 and 13.12 • When you have a significant interaction, interpret mean differences carefully

  16. Figure 13.11

  17. Figure 13.12

  18. Designing a Factorial Study • Each participant in only one IV combo condition • At least 2 levels of each IV • Sometimes more levels is better • Best to have a DV with an interval or ratio scale (easier than nominal/ordinal) • Try for equal n across each tx condition

  19. Estimating Sample Size • Can be accomplished with power analysis • See the appropriate table in Appendix B • Effect size estimate, f • Desired power • Three F-ratios in a two-factor design: A, B, AxB • Plan for sample size needed for weakest effect • Formula for estimating n’ is Equation 13.2

  20. Interpreting Interactions • Residual = effect of interaction after removing influence of the main effects Δij = Mij – Mai – Mbj + Moverall • If interaction not statistically significant then residual (Δij) will be close to 0 • Stronger interactions lead to larger residuals in multiple treatment conditions

  21. Interpreting Interactions • Residuals represent the effects of the interaction on the DV that are not explained by the individual main effects alone • When no interaction is present, the residuals for each treatment condition will be close to or equal to 0 • Table 13.7 and Figure 13.14 illustrate

  22. Table 13.7

  23. Figure 13.14

  24. What is Next? • **instructor to provide details

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