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

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

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? 3

4. Figure 13.1 4

5. GLM and Two-Variable Design Single-variable, X ij = µ + α j + ε ij Now, X ij = µ + α j + β k + αβ jk + ε ijk 5

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 6

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

8. Figures 13.2 & 13.3 8

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 9

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 10

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 11

12. Figure 13.8 12

13. Figure 13.9 13

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

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 15

16. Figure 13.11 16

17. Figure 13.12 17

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 18

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 19

20. Interpreting Interactions Residual = effect of interaction after removing influence of the main effects Δ ij = M ij – M ai – M bj + M overall –If interaction not statistically significant then residual (Δ ij ) will be close to 0 –Stronger interactions lead to larger residuals in multiple treatment conditions 20

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 21

22. Table 13.7 22

23. Figure 13.14 23

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