Statistical Methods for Psychology

Writing this in terms of means and representing adjusted means as , we have

where (the mean preinjection score) and T 1 , T 2 , T 3 , and T 4 are (0, 1, 2 1)

variables. (We substitute the mean Pre score for the individual Pre score because we are

interested in the adjusted means for Yif all subjects had received the mean score on the

covariate.) For our data, the adjusted means of the treatments are:

The adjusted means are plotted in Figure 16.4.

The grand mean is

=2.3075

1 0.8644(0) 1 0.0738(0) 1 0.2183

Y¿.=0.4347(4.8060) 2 0.5922(0) 1 0.0262(0)

=1.9353

1 0.0738( 2 1) 1 0.2183

Y 5 ¿=0.4347(4.8060) 2 0.5922( 2 1) 1 0.0262( 2 1) 1 0.8644( 2 1)

=2.3813

1 0.0738(1) 1 0.2183

Y 4 ¿=0.4347(4.8060) 2 0.5922(0) 1 0.0262(0) 1 0.8644(0)

=3.1719

1 0.0738(0) 1 0.2183

Y¿ 3 =0.4347(4.8060) 2 0.5922(0) 1 0.0262(0) 1 0.8644(1)

=2.3336

1 0.0738(0) 1 0.2183

Y¿ 2 =0.4347(4.8060) 2 0.5922(0) 1 0.0262(1) 1 0.8644(0)

=1.7153

1 0.0738(0) 1 0.2183

Y¿ 1 =0.4347(4.8060) 2 0.5922(1) 1 0.0262(0) 1 0.8644(0)

Pre=4.8060

1 0.0738(T 4 ) 1 0.2183

Y¿j=0.4347(Pre) 2 0.5922(T 1 ) 1 0.0262(T 2 ) 1 0.8644(T 3 )

Y¿j

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

Control

Group

Adjusted mean

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

0.1 μ g 0.5 μ g 1 μ g 2 μ g

Figure 16.4 Adjusted means by group