Many students in psychology are confused by interaction effects in experiments. You can download this Excel workbook to play with some combinations of main and interaction effects. In brief, when you carry out an experiment, you manipulate an independent variable, you measure a dependent variable and you try to control extraneous variables. Let’s use the example of the excellent book and website “Designing and Reporting Experiments in Psychology“ of Peter Harris. You measure the driving performance (dependent variable) for two groups who are equal on extraneous variables as age, motivation, … The first group drives in silence, the second group listens to music while driving. In this particular experiment, there is only one independent variable (music) with two levels or conditions: no music (control group), music (experimental group). That is a single factor experimental design. You can find another (video) example  of a single factor experimental design about attractiveness at the psych files website.

Often, you are interested in more than one factor. Perhaps, you also want to know what the effect of alcohol is on driving performance.  So, you decide to manipulate also this variable.  You distinguish between three conditions: no alcohol, a little bit alcohol, rather much alcohol. Now, you have a two-factor experimental design with 6 independent and different groups of subjects.

• group 1: no music, no alcohol
• group 2: no music, 1 pint of beer
• group 3: no music,  3 pints of beer
• group 4: music, no alcohol
• group 5: music, 1 pint of beer
• group 6: music,  3 pints of beer

Each group contains approximately 20 subjects, in total you need about 120 subjects for this experiment. For each subject, you measure the driving performance, e.g. the duration and  number of errors on a specific track.  The dataset could look like the following table. You can download an example dataset [Excel][PASW].

Nr	alcohol	music	duration	error
1	0	0	120	5
2	0	1	135	7
3	1	1	140	9
4	2	0	135	7

The first subject needed 120 s and made 5 errors on the track. During the ride he or she didn’t listen to music and hadn’t drunk alcohol. The second subject hadn’t drunk any beer before the test drive but was listening to music during the ride. She or he needed 135 s and made 7 errors. The last subject drank three pints of beer (code=2), was not listening to music, made 7 errors and needed 135 s to finish the test.

With software like PASW statistics (Predictive Analytics SoftWare; previously called SPSS Statistical Package for the Social Sciences) it is very easy to calculate the simple effects, e.g. the means for the six conditions in the experiment. Let’s focus on the first dependent variable: duration.

In the above example, there seems to be a main effect of playing music on the driving performance (measured as duration of the test drive). Without music it takes an average of 150 s to complete the test drive, which is 30 s less than the condition with music. Of course, without statistical analysis, we cannot say that this is a significant difference. There also seems to be a mean effect of alcohol. Drinking beer seems to slow down the driving performance. It takes 15 s and 30 s more to complete the test drive when one has drunk 1 or 3 pints of beer.

However, before considering the main effects, we should first take a look at a possible interaction effect. An interaction exists when the effect of one independent variable on the dependent variable changes at the different levels of the second independent variable (Keppel & Wickens, 2004). In our example, this could mean that the effect of music (the second independent variable)  has not the same effect on driving performance at the different levels of the first independent variable: alcohol. May be, music has a more disturbing effect when a subject has drunk 3 pints of beer than when he has drunk 1 pint of beer or no alcohol. You can also formulate this interaction in terms of the first independent variable. Drinking beer has a more disturbing effect on driving when one listens to music.

A researcher should always check first for a possible interaction effect. Most 2-factor studies are carried out because they want to test this interaction; otherwise, it would be much easier to carry out a one-factor experiment. Also, it is not very clear how one should interpret the main effect in light of the interaction.

How can you detect an interaction effect? The easiest way is to graph the results like in the example above. There is no interaction if the lines expressing the simple effects of A at levels of B are superimposed or parallel. If the lines cross (and this could be outside the graph), then there is an interaction effect. Like with the main effect, you should perform a statistical analysis to determine if this effect is significant.

Summarizing: with two independent variables, there are 8 possible situations: main effect A (yes or no); main effect B (yes or no), interaction effect A x B (yes or no). You should consider these possibilities. If you want to visualize this, you can download an Excel workbook, in which you can play with these combinations.

On YouTube, you can find another example of a 2×2 factorial design and a demonstration on how to graph and interpret the interaction in SPSS software.