1. FACTORIAL ANOVA

2. Overview of Factorial ANOVA
Factorial Designs
Types of Effects
Assumptions
Analyzing the Variance
Regression Equation
Fixed and Random Effects

3. FACTORIAL DESIGNS
All combinations of levels of two or more independent variables (factors) are measured

4. Types of Factorials Between subjects (independent)
Within subjects (related)
Mixed

5. Between Subjects A 1 2 1 B 2 Subjects 1-10 Subjects 21-30 Subjects
11-20
Subjects
31-40 2

6. Within Subjects A 1 2 1 B 2 Subjects 1-40 Subjects 1-40 Subjects 1-40

7. Mixed (A Between, B Within)1 2
Subjects
1-20
Subjects
21-40 1 B
Subjects
1-20
Subjects
21-40 2

8. TYPES OF EFFECTS
A main effect is the overall effect of each IV by itself, averaging over the levels of any other IVs.
An interaction occurs when the effects of one factor change depending on the level of another factor.

9. Simple Effects
An interaction can be understood as a difference in simple effects.
A simple effect is the effect of one factor on only one level of another factor.
If the simple effects differ, there is an interaction.

10. 70 60 50 B2
d.v. 40 30 20 B1 10 1 2 A

11. 70 B2 60 50
d.v. 40 B1 30 20 10 1 2 A

12. B2 70 60 50
d.v. 40 30 B1 20 10 1 2 A

13. 70 60 B2 50
d.v. 40 30 20 B1 10 1 2 A

14. ASSUMPTIONS Interval/ratio data Normal distribution or N at least 30
Independent observations
Homogeneity of variance
Proportional or equal cell sizes

15. ANALYZING THE VARIANCE
Total Variance = Model + Residual
Model Variance is further divided into:
Factor A
Factor B
A x B interaction

16. Comparing Variance F-test for each main effect and for the interaction
Each F-test compares variance for the effect to Residual variance

17. REGRESSION EQUATION bo is mean of base group
b1 is the main effect of factor A
b2 is the main effect of factor B
b3 is the A x B interaction

18. FIXED VS. RANDOM EFFECTS
Fixed Factor: only the levels of interest are selected for the factor, and there is no intent to generalize to other levels
Random Factor: the levels are selected at random from the possible levels, and there is an intent to generalize to other levels

19. APA Format Example
The two-way between subjects ANOVA showed a significant main effect of customer type, F(1,1482) = 5.04, p = .025, partial h2 = .00, a non-significant main effect of industry type, F(2,1482) = 0.70, p = .497, partial h2 = .00, and a significant interaction, F(2,1482) = 3.12, p = .044, partial h2 = .00.

20. Take-Home Points Factorial ANOVA allows us to test for interactions.
Most things are affected by multiple factors that do not work independently of each other.