for older ones. The fact that the two lines are not parallel is what we mean when we speak
of an interaction. If Condition differences were the same for the two Age groups, then the
lines would be parallel—whatever differences between Conditions existed for younger par-
ticipants would be equally present for older participants. This would be true regardless of
whether younger participants were generally superior to older participants or whether the
two groups were comparable. Raising or lowering the entire line for younger participants
would change the main effect of Age, but it would have no effect on the interaction because
it would not affect the degree of parallelism between the lines.
It may make the situation clearer if you consider several plots of cell means that repre-
sent the presence or absence of an interaction. In Figure 13.2 the first three plots represent
the case in which there is no interaction. In all three cases the lines are parallel, even when
they are not straight. Another way of looking at this is to say that the simple effect of Fac-
tor Bat is the same as it is at and at. In the second set of three plots, the lines
clearly are not parallel. In the first, one line is flat and the other rises. In the second, the
lines actually cross. In the third, the lines do not cross, but they move in opposite direc-
tions. In every case, the simple effect of Bis notthe same at the different levels of A. When-
ever the lines are (significantly) nonparallel, we say that we have an interaction.A 1 A 2 A 3
422 Chapter 13 Factorial Analysis of Variance
Counting Rhyming Adjective Imagery Intentional
ConditionEstimated Marginal Means of recall68101214161820Estimated Marginal MeansOlder
YoungerAGEFigure 13.1 Cell means for data in Table 13.2Cell meansNo interactionA 2 A 3B 1
B 2A 1 A 2 A 3B 1
B 2A 1 A 2 A 3B 1
B 2A 1Cell meansInteractionA 2 A 3B 1B 2A 1 A 2 A 3B 1B 2A 1 A 2 A 3B 1B 2A 1
Figure 13.2 Illustration of possible noninteractions and interactions