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