Factorial Analysis of Variance Chapter 13 Factorial Analysis of Variance

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

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

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

Recognizing and Interpreting Interaction Effects Graphically

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

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

Figuring a Two-Way ANOVA Sums of squares

Figuring a Two-Way ANOVA Sums of squares

Figuring a Two-Way ANOVA Population variance estimates

Figuring a Two-Way ANOVA Population variance estimates

Figuring a Two-Way ANOVA F ratios

Figuring a Two-Way ANOVA Degrees of freedom

Figuring a Two-Way ANOVA Degrees of freedom

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

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

Effect Size in Factorial ANOVA

Effect Size in Factorial ANOVA

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

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

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

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

Factorial ANOVA in Research Articles A two-factor ANOVA yielded a significant main effect of voice, F(2, 245) = 26.30, p < .001. 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.