Simple Main Effects

Interactions

Suppose an experiment was conducted that examined the consequences of providing different hints for solving the tower of Hanoi problem. The first condition simply provides the rules and the goal for the problem (No hint). The second condition involves telling the participants not to think about moving disks but moving pyramids of disks (Pyramid). The third condition involves telling participants about moving pyramids of disks and states what the first move is (Pyramid + First). The dependent variable is the number of moves to solution of the problem. The results are shown in Figure 1.

These results are explained in terms of reducing the amount of planning that is required. The greater the amount of planning that is necessary, the more mistakes that are made because it is easier to forget long plans.

A different experiment using the tower of Hanoi was also conducted. Three groups were selected according to age: 5–7 years, 9–11 years, and 13–15 years old. Figure 2 shows the results.

The results are also explained with respect to planning such that younger children cannot remember the plans they have made, whereas older children can. In the first experiment, the reduction in planning demands is obtained by changing the representation of the problem. In the second experiment, the ability to deal with planning demands vary according to age. To determine whether reducing the planning demands for younger children by changing the representation of the problem helps them to overcome their problems in planning, the two variables (age and problem representation) are considered at the same time.

Suppose the results shown in Figure 3 were obtained. In this case, the effects of changing the representation of the problem differ with respect to age. In other words, the effects of one variable are different for the different levels of the second variable. This is known as an interaction.

A more formal definition of an interaction is as follows:

Figure 2 The Mean and Standard Errors for Different Ages for Solving the Tower of Hanoi Problem

Figure 3 The Mean and Standard Errors for the Interaction Between Different Ages and Hint Conditions for Solving the Tower of Hanoi Problem

Table 1 An Example ANOVA Output