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Chapter 13

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.

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Chapter 13

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  1. 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 (.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 < .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.

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