1. Chapter 11 Complex ANOVA Designs Part III: Additional Hypothesis Tests Renee R. Ha, Ph.D. James C. Ha, Ph.D Integrative Statistics for the Social & Behavioral Sciences

2. What is a Factorial Design? The simplest factorial design is a 2 × 2 design which involves two independent variables, each with two levels. E.g.: gender (male vs. female) on two levels of a treatment drug (low vs. high).

3. What is a Factorial Design? Factorial designs can involve more levels of each independent variable and thus become a 2 × 3 design, a 3 × 3 design, and so on.

4. Definitions Main effect: Influence of your independent variable on your dependent variable.

5. Definitions Interaction: The combined effect of both (or all) independent variables over and above the separate effects of each variable alone.

6. Figure 11.1 Examples of Main Effects and Interactions in Graphical Form

7. Linear or Additive Equation

8. Table 11.3 SourceSSdfS 2 (MS)F obt. Row (sex) Column (group) Row * Column (sex * group) Within (within a cell) Total Two-Way ANOVA Summary Table (Hesitation Time Example)

9. Types of Variance

10. F-obtained Formulas

11. Figure 11.2 Craik and Lockhart (1972) Memorization Experiment

12. Results if you use Microsoft Excel to calculate the Two-way ANOVA Anova: Two-Factor ANOVA Source of VariationSSDfMSFP-valueF crit Sample249.641 35.730916034.4838E-083.946865945 Columns1476.664369.16552.838501917.85493E-232.472930305 Interaction195.26448.8156.9868797716.04944E-052.472930305 Within628.890 6.986666 7 Total 2550.3 699

13. Results if you use SPSS to calculate the ANOVA (or F test) Tests of Between-Subjects Effects Dependent Variable: SCORE Source Type III Sum of Squares dfMean SquareFSig. Model15331.200101533.120219.435.000 AGE249.6401 35.731.000 TECH1476.6604369.16552.839.000 AGE * TECH195.260448.8156.987.000 Error628.800906.987628.800 Total15960.000100

14. Figure 11.3

15. Results if you use Microsoft Excel to calculate the Two-way ANOVA ANOVA Source of VariationSSdfMSFP-valueF crit Sample30.33333215.166671.952790.1537153.20432 Columns254.33332127.166716.373394.54E-063.20432 Interaction13.3333343.3333330.4291850.7867692.578737 Within349.5457.766667 Total647.553

16. Results if you use SPSS to calculate the ANOVA (or F test) Tests of Between-Subjects Effects Dependent Variable: EYEGLAN Source Type III Sum of SquaresdfMean SquareFSig. Model 298.000837.2504.796.000 DISCTYP 30.333215.1671.953.154 PAIRGEN 254.3332127.16716.373.000 DISCTYP * PAIRGEN 13.33343.333.429.787 Error 349.500457.767 Total 701.00054

17. When to Use Two-Way ANOVA? 1. You have two independent variables and a between- groups (independent groups) design, and 2. The sampling distribution is normally distributed, and 3. The dependent variable is on an interval or ratio scale (typically), and 4. When the variances of the groups are the same, or are homogeneous.

18. Multifactorial ANOVA Also called MANOVA

19. Repeated-Measures ANOVA

20. When to Use a RM ANOVA? 1. You have one independent variable with more than two levels and a within-groups design. 2. The sampling distribution is normally distributed. 3. The dependent variable is on an interval or ratio scale (typically).

21. Overview of Single-Sample, Two-Sample, and Three or More Sample Tests