Interaction (7 of 8)
Higher Order Interactions
So far, all the interactions that have been described are called
"two-way" interactions. They are two-way interactions because they
involve the interaction of two variables. A three-way interaction is
an interaction among three variables.
There is a
three-way interaction whenever a two-way interaction differs depending
on the level of a third variable. Consider the two figures on the left
side of this page. The upper figure shows the interaction between task
and condition (B) for well-rested subjects; the lower figure shows the
same interaction for sleep-deprived subjects. The forms of these interactions
are different. For the well-rested subjects, the difference between Tasks 1
and 2 is largest under condition B2 whereas for the sleep-deprived
subjects the difference between Tasks 1 and 2 is smallest under condition B2.
The two-way interactions are therefore different for the two levels of the
variable "sleep deprivation." This means that there
is a three-way interaction among the variables sleep deprivation, task,
and condition.