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ANOVA: Notes on Understanding Interaction

Last updated:
27 Apr 2005

Some notes that might help in grasping ANOVA interactions:

  • Interaction means that the IVs are not independent.  The IVs have a complex (interactive) influence on the DV. 

  • An interaction means that the main effects can not be relied upon to tell the full story.  When there is an interaction effect, it means the main effects do not collectively explain all of the influence of the IVs on the DV.  The IVs have an interactive effect on the DV, which means the cell means must be examined for each sub-group -- this is where the nature / direction of the interaction can be found.

  • Interaction in ANOVA is equivalent to interaction in MLR.

  • Understanding of interaction can be pursued mathematically or it be grasped graphically.  It is easiest to depict using a 2x2 factorial, mixed or within-subjects design.  Interaction is indicated by non-parallel lines in a line graph.  In other words, if the lines are crossed or would eventually cross if extended, then there is an interaction.  Of course the lines are rarely perfectly parallel, so the real question is about whether the different pattern of means across the sub-groups is to be considered unlikely to have occurred by chance.  The significance test of the interaction and its associated effect size are the key pieces of information.  The figure below shows some possible outcomes of the experiment investigating the effects of intensity of exercise and time of day on amount of sleep.

  • Make when interpreting interaction to describe the direction of any relationships.

  • Further reading....Two-way analysis of variance (University of New England)