C More on main effects, interactions, and graphing interactions

C1 Main effects of independent variables

A useful way of thinking about experiments employing more than one IV is to think of them as if they were several experiments being run simultaneously. The number of experiments being run corresponds to the number of separate IVs.

Table C1
A Two-by-Two Design to Test the Effects of Music and Alcohol on Driving Performance

For example, imagine that we ran the driving study described in the book (e.g., Section 13.2) to examine the effects of both music and alcohol as depicted in Table C1. You can think of this design as involving two separate experiments in one. In one of the experiments we examine whether listening to music affects driving performance. In the other experiment, we examine whether consuming alcohol affects driving performance. Thus, at the end of this experiment, we would be able to say whether driving performance differed in the music on condition when compared with the music off condition. Moreover, at the end of this experiment we would also be able to say whether driving performance varied in the alcohol condition from that in the no alcohol condition. That is, we would be able to compare the overall driving performance of our participants in the music on versus the music off condition by averaging over the alcohol and no alcohol conditions. Likewise, we would be able to compare the overall driving performance of those who had drunk alcohol with the overall driving performance of those who had not drunk alcohol, by averaging over their performance in the music on and the music off conditions.

Say that we find that listening to music makes a difference to driving performance: that drivers perform significantly better when they do not listen to music than they do when they do listen to music. We refer to such an effect as a significant main effect of the IV. The main effect of an IV is the effect of that IV on the DV ignoring the other IVs in the experiment. Here, we would thus have found a significant main effect of listening to music on driving performance. Likewise, if we find that drivers perform significantly better when they have not drunk alcohol than when they have drunk alcohol, we would also have a main effect of drinking alcohol on driving performance. Our experiment would thus have two main effects. However, if the effects of alcohol were not significant we would say that there was no significant main effect of alcohol on driving performance and the experiment would have only one significant main effect.

Main effects are essentially the findings of the single experiment involving that IV. Thus there is potentially a significant main effect for every IV in the experiment (see Section C7 of this Web site for a list of the potential main effects in designs with 2-4 IVs). A main effect is what I describe in the experiments in Chapters 9 and 10 of the book - e.g., finding that eating cheese affects the number of nightmares, that listening to music affects driving performance, or that drinking alcohol affects driving performance.

If we ran an experiment involving three IVs, this would be like running three experiments simultaneously. We could thus test for three main effects – one for each of the IVs in the design (see Section 3.7 of this website).

Table C2
The Marginal Means

Note. c = condition

Significant main effects are what we find when there are statistically significant differences between the overall means for the IV. The means for the main effects are known in the trade as the marginal means to tell them apart from the means that are involved in the interaction effect. The marginal means are the means for the rows or columns in the table. Looking at Table C2, the main effect of music indicates that the mean for the music off condition, Marginal Mean 1, is significantly different from the mean for the music on condition, Marginal Mean 2. The main effect of alcohol indicates that the mean for the no alcohol condition, Marginal Mean 3, is significantly different from the mean for the alcohol condition, Marginal Mean 4.

Table C3
An Example Showing Marginal Means

For example, Table C3 contains some possible (but hypothetical) marginal means for the alcohol and music experiment. Looking at Table C3, you can see that there is unlikely to be a significant main effect of music as Marginal Mean 1, the mean for the music off condition (9.0), is unlikely to be significantly different from the mean for the music on condition, Marginal Mean 2 (9.4). However, there is likely to be a significant main effect of alcohol, as participants in the no-alcohol condition are making more than twice the number of errors, on average, than those in the alcohol condition. That is, Marginal Mean 4 (12.4) is more than twice Marginal Mean 3 (6.0). (I am assuming that the experiment has medium power – see Chapter 12 of the book for a discussion of power.)

Summary