Factorial design activity: Graphing cell means to visualize main effects and interactions

The numbers in the black boxes represent group means in a 2 x 2 design.  The marginal means for factors A and B are also shown.  The cell means are plotted as line graphs and as bar graphs.

The four graphs all show the same cell means.  On the left, the two levels of factor A are on the x-axis, with different lines or bars representing the levels of factor B.  The two graphs on the right show factor B on the x-axis.

Why do the left and right graphs sometimes look so different? Which one of the four graphs do you think best communicates the results?

Change the cell means to produce . . .

•  an A x B interaction, but no main effects;
•  a main effect for A, but no main effect for B, and no interaction;
•  two main effects, but no interaction;
•  an interaction, and a main effect for B;
•  no main effects, and no interaction.

Click the New data button:

• Are there any main effects?
• Is there an interaction?  If so, can you describe it in plain English?
• Before looking at the graphs, draw your own graph of the cell means.  Does your graph match the corresponding one below?

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Notes
This activity is based, in part, on a computer program described in: Strube, M. J., & Goldstein, M. D. (1995). A computer program that demonstrates the difference between main effects and interactions.  Teaching of Psychology, 22, 207-208.
The graphs are made with jQuery (jquery.com) and Flot (flotcharts.org).