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Some possible outcomes for the experiment in Table C1 are illustrated in Figures C1-C4.
In Figure C1, you can see that there is the same difference between Cell Mean A and Cell Mean C as there is between Cell Mean B and Cell Mean D. That is, alcohol makes the same difference to performance whether or not the participant is listening to music. The variables do not interact. Here we have only a main effect of alcohol: performance is worse after alcohol. Listening to music makes no difference to performance.
In Figure C2 again alcohol makes the same difference to performance whether or not the participant is listening to music. Yet again, there is the same difference between Cell Mean A and Cell Mean C as there is between Cell Mean B and Cell Mean D. So, the variables do not interact. However, this time there is also a main effect of listening to music. That is, we can see that the marginal mean for the errors made when listening to music will be higher than the marginal mean for the errors made with no music (i.e., Marginal Mean 2 is higher than Marginal Mean 1). (If you do not understand what I mean by a marginal mean, see Section C1 of this Web site.)
In Figure C3, the effects of music are inconsistent. Music makes a bigger difference to performance when participants have been drinking alcohol than it does when they have not been drinking alcohol. That is, there is a bigger difference between Cell Mean B and Cell Mean D than there is between Cell Mean A and Cell Mean C. The effect of music is to exacerbate the effect of alcohol on driving performance. As you can imagine, this interaction is interesting. It tells us something that we did not know. Alcohol and music interact. They compound each other’s effect. (Note that here we also have main effects of both IVs. That is, Marginal Mean 2 will be bigger than Marginal Mean 1 and Marginal Mean 4 will be bigger than Marginal Mean 3.) (If you do not understand what I mean by a marginal mean, see Section C1 of this Web site.)
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