Statistical Methods for Psychology

Applying this procedure to all cells we obtain the following adjusted cell means

These are the cell means given in Exhibit 16.5, and the row and column means can be

found as the mean of the cells in that row or column.

Testing Adjusted Means

The adjusted means are plotted in Figure 16.5. They illustrate the interaction and also the

meaning that may be attached to the main effects. Further analyses of these data are proba-

bly unnecessary because differences due to smoking seemed to be confined to the condition

that requires high levels of cognitive processing. However, for the sake of completeness we

will assume that you wish to make a comparison between the mean of the NonSmoking

group and the combined means of the Active and Delayed groups. In this case you want

to compare with and combined. This comparison requires some modification of

the error term, to account for differences in the covariate. This adjustment is given by

Winer (1971) as

where and represent the sum of squares attributable to Groups and Error

(respectively) in an analysis of variance on the covariate, and is the error term from

the overall analysis of covariance.

MS¿error

SSg(c) SSe(c)

MS–error=MS¿error

C

11

SSg(c)

g 21

SSe(c)

S

X1.¿ X2.¿ X¿3.

Pattern Rec Cognitive Driving Row Means

NonSmokers 9.805 27.770 8.505 15.360

Delayed 9.732 40.436 8.921 19.696

Active 9.558 43.785 5.820 19.721

Column Means 9.699 37.330 7.749 18.259

Section 16.9 The Factorial Analysis of Covariance 619

Smoking group

NonSmokers Delayed Smokers Active Smokers

Estimated marginal means

50

40

30

20

10

0

Task

Cognitive

Driving

Patrecog

Figure 16.5 Adjusted cell means as a function of Group and Task