Interaction (7 of 8)

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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.
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