Many people will argue that if you find a significant interaction, the main effects
should be ignored. It is not reasonable, however, automatically to exclude interpretation of
main effects in the presence of anysignificant interaction. In the Eysenck study, we had a
significant interaction, but for both younger and older participants the tasks that involved
greater processing led to greater recall. The fact that this effect was more pronounced in
the younger group does not negate the fact that it was also clearly present in the older par-
ticipants. Here it is perfectly legitimate to speak about the main effect of Condition, even
in the presence of an interaction, though you should also be quick to point out that Condi-
tion effects also depend on the Age of the participant. However, had the younger group
shown better recall with more demanding tasks whereas the older group had shown poorer
recall, then it might actually not be of interest whether the main effect of Condition was
significant or not, and we would instead concentrate on discussing only the simple effects
of difference among Conditions for the younger and older participants separately. (Interac-
tions in which group differences reverse their sign at some level of the other variable are
sometimes referred to as “disordinal”interactions.When one group is consistently above
the other group we have an “ordinal”interaction.) In general, the interpretation depends
on common sense. If the main effects are clearly meaningful, then it makes sense to inter-
pret them, whether or not an interaction is present. However, if the main effect does not
really have any meaning, then it should be ignored.
This discussion of the interaction effects has focused on examining cell means. I have
taken that approach because it is the easiest to see and has the most to say about the results
of the experiment. Rosnow and Rosenthal (1989) have pointed out that a more accurate
way to look at an interaction is to first remove any row and column effects from the data.
They raise an interesting point, but most interactions are probably better understood in
terms of the explanation above.13.4 Simple Effects
I earlier defined a simple effect as the effect of one factor (independent variable) at one
level of the other factor—for example, the differences among Conditions for the younger
participants. The analysis of simple effects can be an important technique for analyzing
data that contain significant interactions. In a very real sense, it allows us to “tease apart”
interactions.
I will use the Eysenck data to illustrate how to calculate and interpret simple effects.
Table 13.4 shows the cell means and the summary table reproduced from Table 13.2. The
table also contains the calculations involved in obtaining all the simple effects.
The first summary table in Table 13.4c reveals significant effects due to Age, Condi-
tion, and their interaction. We already discussed these results earlier in conjunction with
the original analysis. As I said there, the presence of an interaction means that there are dif-
ferent Condition effects for the two Ages, and there are different Age effects for the five
Conditions. It thus becomes important to ask whether our general Condition effect really
applies for older as well as younger participants, and whether there really are Age differ-
ences under all Conditions. The analysis of these simple effects is found in Table 13.4b and
the second half of Table 13.4c. I have shown all possible simple effects for the sake of com-
pleteness of the example, but in general you should calculate only those effects in which
you are interested. When you test many simple effects you either raise the familywise error
rate to unacceptable levels or else you control the familywise error rate at some reasonable
level and lose power for each simple effect test. One rule of thumb is “Don’t calculate a
contrast or simple effect unless you plan to discuss it when you write up the results.” The
more effects you test, the higher the familywise error rate will be.Section 13.4 Simple Effects 423disordinal
interactions
ordinal
interaction