Statistical Methods for Psychology

This decrement is the sum of squares attributable to the main effect of A. By the same reasoning, we can obtain by comparing for ...

Section 16.5 The One-Way Analysis of Covariance 599 Exhibit 16.3 Abbreviated SAS analysis of the data in Table 16.7 Data Nonorth ...

(the covariate), we would have a clearer test of our original hypothesis. This is exactly what the analysis of covariance is des ...

Calculating the Analysis of Covariance When viewed within the framework of multiple regression, the analysis of covariance is ba ...

The full model (including the interaction predictors) states that where represents the treatment effect for the jth treatment, c ...

The regression analysis of this model would produce If there is no significant difference in within-treatment regressions—that i ...

variation that cannot be defined by the treatment effect. In other words, we will take the model with both the covariate and tre ...

from the full model and the other sums of squares are as calculated before. Notice also that there is one degree of freedom for ...

Writing this in terms of means and representing adjusted means as , we have where (the mean preinjection score) and T 1 , T 2 , ...

which is the mean of the adjusted means. (In a case in which we have equal sample sizes, the adjusted grand mean will equal the ...

608 Chapter 16 Analyses of Variance and Covariance as General Linear Models Estimated Marginal Means Treatment Group Dependent V ...

16.6 Computing Effect Sizes in an Analysis of Covariance As you might expect, computing effect sizes is a bit more complicated i ...

suggesting a choice. If the covariate naturally varies in the population (as it does in this case, where we expect different ani ...

of the original measurements. (Recall that we used SStotalfrom the analysis of variance when we calculated h^2 .) An alternative ...

the two groups to have the same mean on the posttest in the absence of a real treatment effect. Huitema (1980, pp. 149ff) gives ...

The logic of the analysis is straightforward and follows that used in the previous ex- amples. is the variation attributable to ...

614 Chapter 16 Analyses of Variance and Covariance as General Linear Models Table 16.11 Hypothetical data on smoking and perform ...

If we drop the interaction terms representing the interaction of the covariate (Distract) with the Task 3 Group interaction, we ...

616 Chapter 16 Analyses of Variance and Covariance as General Linear Models Table 16.13 Regression results for various models fo ...

Section 16.9 The Factorial Analysis of Covariance 617 Type III Sum of Squares 36389.602b 892.395 4644.876 23870.485 563.257 1626 ...