Statistical Methods for Psychology

The full model (including the interaction predictors) states that

where represents the treatment effect for the jth treatment, crepresents the covariate,

represents our term testing homogeneity of regression, and represents the error associ-

ated with the ith subject in treatment j.

We can compare two models either on the basis of the change in between the

two models (using the residual from the more complete model for our error term), or on

the basis of the decrease in R^2. In this case the latter is somewhat simpler.

SSregression

eij

tj ctj

Yij=tj 1 c 1 ctj 1 eij

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

Table 16.7 Pre- and postinjection data from Conti and Musty (1984)

Control 0.1 mg 0.5 mg1 mg2 mg

Pre Post Pre Post Pre Post Pre Post Pre Post

4.34 1.30 1.55 0.93 7.18 5.10 6.94 2.29 4.00 1.44

3.50 0.94 10.56 4.44 8.33 4.16 6.10 4.75 4.10 1.11

4.33 2.25 8.39 4.03 4.05 1.54 4.90 3.48 3.62 2.17

2.76 1.05 3.70 1.92 10.78 6.36 3.69 2.76 3.92 2.00

4.62 0.92 2.40 0.67 6.09 3.96 4.76 1.67 2.90 0.84

5.40 1.90 1.83 1.70 7.78 4.51 4.30 1.51 2.90 0.99

3.95 0.32 2.40 0.77 5.08 3.76 2.32 1.07 1.82 0.44

1.55 0.64 7.67 3.53 2.86 1.92 7.35 2.35 4.94 0.84

1.42 0.69 5.79 3.65 6.30 3.84 5.69 2.84

1.90 0.93 9.58 4.22 5.54 2.93

Mean 3.377 1.094 5.387 2.586 6.494 3.906 5.045 2.485 3.943 1.560

Design Matrix

Cov T 1 T 2 T 3 T 4 CT 1 CT 2 CT 3 CT 4

4.34 1 0 0 0 4.34 0 0 0 1.30

... ... ... ... ... ... ... ... ... ...

1.90 1 0 0 0 1.90 0 0 0 0.93

1.55 0 1 0 0 0 1.55 0 0 0.93

... ... ... ... ... ... ... ... ...

9.58 0 1 0 0 0 9.58 0 0 4.22

7.18 0 0 1 0 0 0 7.18 0 5.10

X 5 ... ... ... ... ... ... ... ... ... Y 5 ...

(47 3 9) 6.30 0 0 1 0 0 0 6.30 0 (47 3 1) 3.84

3.94 0 0 0 1 0 0 0 6.94 2.29

... ... ... ... ... ... ... ... ... ...

7.35 0 0 0 1 0 0 0 7.35 2.35

4.00 21 21 21 21 2 4.00 2 4.00 2 4.00 2 4.00 1.44

... ... ... ... ... ... ... ... ...

5.54 21 21 21 21 2 5.54 2 5.54 2 5.54 2 5.54 2.93