Statistical Methods for Psychology

As an illustration, we will consider a case of a 2 3 4 factorial with four subjects per cell.

Such a design is analyzed by the conventional analysis of variance in Table 16.2, which also

includes means, estimated effects, and values of. From the summary table, it is apparent

that the main effect of Bis significant but that the effects of Aand ABare not.

To analyze these data from the point of view of multiple regression, we begin with the

following design matrix. Once again, the elements of each row apply to all subjects in the

corresponding treatment combination.

h^2

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

Table 16.2 Sample data and summary table for factorial design

(a) Data

B 1 B 2 B 3 B 4 Means

52811

A 1 7 5 11 15

9 7 12 16

8 3 14 10

7.25 4.25 11.25 13.00 8.92750

73911

A 2 9 8 12 14

10 9 14 10

911 812

8.75 7.75 10.75 11.75 9.75000

Means 8.000 6.000 11.000 12.375 9.34375

(b) Summary Table

Source df SS MS F

A 1 5.282 5.282 , 1 .014

B 3 199.344 66.448 11.452* .537

AB 3 27.344 9.115 1.571 .074

Error 24 139.250 5.802

Total 31 371.220

*p,.05

(c) Estimated Treatment Effects

ab 13 =AB 132 A 12 B 31 X..=11.2500 2 8.9375 2 11.0000 1 9.34375=0.65625

ab 12 =AB 122 A 12 B 21 X..=4.2500 2 8.9375 2 6.0000 1 9.34375= 2 1.34375

ab=AB 112 A 12 B 11 X..=7.2500 2 8.9375 2 8.0000 1 9.34375= 2 .34375

bN 3 =B 32 X..=11.0000 2 9.34375=1.65625

bN 2 =B 22 X..=6.0000 2 9.34375= 2 3.34375

bN 1 =B 12 X..=8.0000 2 9.34375= 2 1.34375

aN 1 =A 12 X..=8.9375 2 9.34375= 2 0.40625

mN =9.34375

h^2

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