What is an interaction effect?

Two independent
variables interact if the effect of one of the variables differs
depending on the level of the other variable. The means from the
hypothetical experiment described in the section on
factorial designs are reproduced below. Notice that the effect of drug dosage differs depending on whether the task is simple or complex. For the simple task, the higher the dosage, the shorter the time to complete the task. For the complex task, the higher the dosage, the longer the time to complete the task. Thus, there is an interaction between dosage and task complexity. It is usually much easier to interpret an interaction from a graph than from a table. A graph of the means for the interaction between task complexity and drug dosage is shown on the next page. The dependent variable (response time) is shown on the Y axis. The levels of drug dosage are shown on the X axis. The two levels of task complexity are graphed separately.
Two variables interact if a particular
combination of variables leads to results that would not be anticipated on
the basis of the main effects of those
variables. For instance, it is known that both drinking alcohol and smoking
increase the chance of throat cancer. However, people who both drink and
smoke have a much higher chance of getting cancer than would be predicted if
one knew only how much more likely smokers are than nonsmokers to get throat
cancer and how much more likely drinkers are than nondrinkers to get throat
cancer. The combination of smoking and drinking is particularly dangerous:
these drugs interact. This definition of interaction in terms of a
particular combination of variables is consistent with the previously-given
definition that there is an interaction if the effect of one variable
differs depending on the level of another variable. In the tobacco and
alcohol example, the effect of smoking on the probability of getting cancer
is greater for people who drink than for people who do not drink: the effect
of smoking differs depending on whether drinkers or nondrinkers are being
considered. Similarly, the effect of drinking differs depending on whether
smokers or nonsmokers are being considered. a.
Overall, Condition B
In
Example 4 there is no interaction. The effect of task is the same at all
three levels of B and the effect of B is the same for both tasks. Notice
that the two lines are parallel. When there is no interaction, the lines
will always be parallel.
Four-way interactions occur when three-way interactions differ as a function of the level of a fourth variable. Four-way and higher interactions are usually very difficult to interpret and are rarely meaningful. Note that an interaction effect limits the generalizability of a main effect! Read more about this in the section about simple effects. |

Reference:

http://davidmlane.com/hyperstat/