Interactions
An effect of interaction
occurs when a relation between (at least) two variables is modified by
(at least one) other variable. In other words, the strength or the sign
(direction) of a relation between (at least) two variables is different
depending on the value (level) of some other variable(s). (The term interaction
was first used by Fisher, 1926). Note that the term "modified"
in this context does not imply causality but represents a simple fact
that depending on what subset of observations [regarding the "modifier"
variable(s)] you are looking at, the relation between the other variables
will be different.
For example, imagine that we have a sample of highly achievementoriented
students and another of achievement "avoiders." We now create
two random halves in each sample, and give one half of each sample a challenging
test, the other an easy test. We measure how hard the students work on
the test. The means of this (fictitious) study are as follows:

Achievementoriented 
Achievementavoiders 
Challenging Test 
10 
5 
Easy Test 
5 
10 
How can we summarize these results? Is it appropriate to
conclude that 1) challenging tests make students work harder, and 2) achievementoriented
students work harder than achievementavoiders? None of these statements
captures the essence of this clearly systematic pattern of means. The
appropriate way to summarize the result would be to say that challenging
tests make only achievementoriented students work harder, while easy
tests make only achievementavoiders work harder. In other words, the
relation between the type of test and effort is positive in one group
but negative in the other group. Thus, the type of achievement orientation
and test difficulty interact in their effect on effort; specifically,
this is an example of a twoway interaction between achievement orientation
and test difficulty. (Note that statements 1 and 2 above would describe
socalled main effects.)
For more information regarding interactions, see Interaction
Effects.