Statistical Methods for Psychology

variation that cannot be defined by the treatment effect. In other words, we will take the

model with both the covariate and treatment predictors and compare it to a model with only

the treatment predictors. The difference in the two sums of squares due to regression will

be the sum of squares that the covariate accounts for over and abovewhat is accounted for

by treatment effects. For our data, this is

We now have all the information necessary to construct the analysis of covariance sum-

mary table. This is presented in Table 16.9. Notice that in this table the error term is

=38.3407

=82.6435 2 44.3028

SScovariate=SSregressiont,c 2 SSregressiont

604 Chapter 16 Analyses of Variance and Covariance as General Linear Models

Table 16.8 Regression analysis

(a) Full Model

Analysis of Variance Summary Table for Regression

Source df SS MS F

Regression 5 82.6435 16.5287 33.6726

Residual 41 20.1254 0.4909

Total 46 102.7689

(b) Reduced Model—Omitting Treatment Predictors

Analysis of Variance Summary Table for Regression

Source df SS MS F

Regression 1 73.4196 73.4196 112.5711

Residual 45 29.3493 0.6522

Total 46 102.7689

(c) Reduced Model—Omitting Covariate (Pre)

Analysis of Variance Summary Table for Regression

Source df SS MS F

Regression 4 44.3028 11.0757 7.9564

Residual 42 58.4661 1.3921

Total 46 102.7689

R^2 c=.4311

YNij= 2 1.2321(T 1 ) 1 0.2599(T 2 ) 1 1.5794(T 3 ) 1 0.1589(T 4 ) 1 2.3261

R^2 c=.7144

YNij=0.5311(Pre) 2 0.26667

R^2 t,c=.8042

YNij=0.4347(Pre) 2 0.5922(T 1 ) 1 0.0262(T 2 ) 1 0.8644(T 3 ) 1 0.0738(T 4 ) 1 0.2183