1. Factorial Analysis of Variance
Chapter 13
Factorial Analysis of Variance

2. Basic Logic of Factorial Designs and Interaction Effects
Factorial research design
Effect of two or more variables examined at once
Efficient research design
Interaction effects
Combination of variables has a special effect

3. Basic Logic of Factorial Designs and Interaction Effects
Two-way analysis of variance
One-way analysis of variance
Main effect
Cell
Cell mean
Marginal means

4. Recognizing and Interpreting Interaction Effects
Words
Interaction effect occurs when the effect of one variable depends on the level of another variable
Numbers

5. Recognizing and Interpreting Interaction Effects
Graphically

6. Basic Logic of the Two-Way ANOVA
The three F ratios
Column main effect
Row main effect
Interaction effect
Logic of the F ratios for the row and column main effects
Logic of the F ratio for the interaction effect

7. Figuring a Two-Way ANOVA
Structural model for the two-way ANOVA
Each score’s deviation from the grand mean
Score’s deviation from the mean of its cell
Score’s row’s mean from the grand mean
Score’s column’s mean from the grand mean
Remainder after other three deviations subtracted from overall deviation from grand mean

8. Figuring a Two-Way ANOVA
Sums of squares

9. Figuring a Two-Way ANOVA
Sums of squares

10. Figuring a Two-Way ANOVA
Population variance estimates

11. Figuring a Two-Way ANOVA
Population variance estimates

12. Figuring a Two-Way ANOVA
F ratios

13. Figuring a Two-Way ANOVA
Degrees of freedom

14. Figuring a Two-Way ANOVA
Degrees of freedom

15. Figuring a Two-Way ANOVA
ANOVA table for two-way ANOVA

16. Assumptions in Two-Way ANOVA
Populations follow a normal curve
Populations have equal variances
Assumptions apply to the populations that go with each cell

17. Effect Size in Factorial ANOVA

18. Effect Size in Factorial ANOVA

19. Power for Studies Using 2 x 2 or 2 x 3 ANOVA (.05 significance level)

20. Approximate Sample Size Needed in Each Cell for 80% Power (
Approximate Sample Size Needed in Each Cell for 80% Power (.05 significance level)

21. Extensions and Special Cases of the Factorial ANOVA
Three-way and higher ANOVA designs
Repeated measures ANOVA

22. Controversies and Limitations
Unequal numbers of participants in the cells
Dichotomizing numeric variables
Median split

23. Factorial ANOVA in Research Articles
A two-factor ANOVA yielded a significant main effect of voice, F(2, 245) = 26.30, p < As expected, participants responded less favorably in the low voice condition (M = 2.93) than in the high voice condition (M = 3.58). The mean rating in the control condition (M = 3.34) fell between these two extremes. Of greater importance, the interaction between culture and voice was also significant, F(2, 245) = 4.11, p < .02.