|
Interaction effects like those depicted in Figure C3 occur when the variables in combination produce effects that are bigger in magnitude but in the same direction as their effects alone. Interactions between IVs can also occur when the effect of the level of one IV is opposite at the levels of the other – as depicted in Figure C4. Here listening to music counteracts the impact of alcohol. For some reason, music impairs the driving performance of those who have not been drinking alcohol. (Perhaps it distracts them.) However, it improves the driving performance of those who have been drinking alcohol. (Perhaps it calms them down or helps to focus their attention.) Nevertheless, we still have an interaction between the IVs. The effect of music is inconsistent at the levels of the alcohol IV.
However, in this case, because the effects of music are opposite and approximately equal at the levels of the alcohol IV, there are no significant main effects. That is, in this case, the marginal means for alcohol and no alcohol are unlikely to be very different from each other. The same is likely to be true for the marginal means for music and no music. The effects more or less cancel each other out. Thus we have here an interaction but no main effects.
Under these circumstances we would have to be very cautious when talking about the absence of main effects in our data. Why? Because we know from the data that alcohol does affect driving (making it worse when people are not listening to music but better when they are). Likewise, we know from the data that music does affect driving (making it worse when people have not been drinking alcohol but better when they have been drinking alcohol). This illustrates an important point for interpreting data from studies involving more than one IV. Significant interactions qualify main effects of the IVs involved in the interaction. In this case, what we say about the overall effect of alcohol or music is qualified. We know that we can be more accurate if we talk about the effects of alcohol and music in combination. In this case, the interaction represents an improvement in our knowledge over any statements that we make about the main effects. We therefore qualify any statements that we make about the absence of main effects and give precedence to the interaction when discussing the findings. (Note that this is also true if there are significant main effects. The presence of a significant interaction always qualifies a main effect because it provides more specific information about the effects of the IVs involved.)
Several other points I hope are also clear from this discussion. First, when it comes to the analyses, you can find statistically significant main effects, statistically significant interactions, or both. Second, graphing significant interactions can be a very useful aid to interpreting them. This has been clear for even the 2 x 2 design discussed here. It is even more so when you have more levels on your IVs or more IVs involved in the interaction (or both). (For more on when and how to use graphs in your reports see sections 8.5 and 13.7 of the book.)
|
