1. The Structural Model in the
Chapter 12
The Structural Model in the
Analysis of Variance

2. The Structural Model
Flexible way of figuring the two population variance estimates
Handles situation when sample sizes in each group are not equal
Insight into underlying logic of ANOVA

3. Principles of the Structural Model
Dividing up the deviations
Deviation of a score from the grand mean
Deviation of the score from the mean of its group
Deviation of the mean of its group from the grand mean
Summing the squared deviations

4. Principles of the Structural Model
From the sums of squared deviations to the population variance estimates

5. Principles of the Structural Model
Relation of the structural model approach to the Chapter 11 approach
Within-groups variance estimate
Never figure the variance estimate for each group and average them
Between-groups variance estimate
Never multiply anything by the number of scores in each sample
Same ingredients for the F ratio

6. Principles of the Structural Model
Relation of the structural model approach to the Chapter 11 approach
Chapter 11
Emphasizes entire groups
Focuses directly on what contributes to the overall population variance estimates
Structural model
Emphasizes individual scores
Focuses directly on what contributes to the divisions of the deviations of scores from the grand mean

7. Using the Structural Model to Figure an ANOVA
Example analysis of variance table

8. Analysis of Variance Table

9. Post-Hoc Comparisons Exploratory approach Scheffé test
Figure the F in the usual way
Divide the F by the overall study’s dfBetween
Compare this to the overall study’s F cutoff

10. Effect Size for ANOVA
Proportion of variance accounted for (R2)

11. Effect Size for ANOVA R2 also known as η2 (eta squared) small R2 = .01
medium R2 = .06
large R2 = .14

12. Power for ANOVA (.05 significance level)

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

14. Controversies and Limitations
Normal population distributions
Equal population variances
Independence
Each score is independent of the others
Unit of analysis

15. Reporting in Research Articles