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Advanced Concepts in Factorial ANOVA Studies

Understand the intricacies of factorial ANOVA designs, interaction effects, and power analysis. Explore controversial applications and extensions of multifactorial studies.

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Advanced Concepts in Factorial ANOVA Studies

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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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