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

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

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

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

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

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

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

Analysis of Variance Table

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

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

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

Power for ANOVA (.05 significance level)

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

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

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