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Once we have more than one IV in an experiment we can also test for interactions between the IVs. My students often struggle with understanding interactions. Yet, when you first start designing your own studies in psychology you are in fact naturally very aware of interactions. Remember those first studies in which you wanted to include all the variables that you could think of – from ethnic background, social class, time of day of measurement, gender of participant, gender of experimenter, temperature in the room, what the participants had for breakfast and so on – as well as the main variables of interest? This reflects your natural, intuitive awareness that these variables may well make a difference to the effects. That is, you are concerned that the effect of the variables of interest may be changed – accentuated, reduced or even eliminated – by the presence of these additional variables. That is what an interaction tells us – that the effects of an IV are different – accentuated, reduced or even eliminated – at the levels of another IV. I have never understood why, within a year or so, many students have lost this natural, intuitive understanding and are bewildered by the notion of one IV interacting with another.
Cell Mean A |
Cell Mean B |
Cell Mean C |
Cell Mean D |
Interactions involve the cell means, not the marginal means. Cell means are the means for the IVs in combination. For example, the cell mean that I have called Cell Mean A in Table C4 is the score for participants driving without alcohol and with no music. (In a related measures experiment this would be the baseline condition – our measure of the basic level of performance by participants without the levels of the IV that might make a difference to their performance, in this case alcohol or music.) In a factorial experiment there are as many cells as there are possible combinations of the levels of the IVs in that experiment. In this case, because we have a 2 x 2 design, there are four cells. (For more on different types of design, see Chapters 10 and 13 of the book.)
- How many cells would there be in a 2 x 3 x 3 factorial design?
Click here for the answer
In experiments involving more than one IV, as well as looking for differences between the marginal means, therefore, we can also look at differences between the cell means. In particular, we are interested in the pattern of the differences between the cell means. For example, is the size and direction of the difference between Cell Mean A and Cell Mean C in Table C4 more or less the same as the size and direction of the difference between Cell Mean B and Cell Mean D? That is, does drinking alcohol make approximately the same difference to performance when not listening to music (Cell Mean A minus Cell Mean C) as it does when listening to music (Cell Mean B minus Cell Mean D)? If it does not, then the IVs interact. That is, the effects of the alcohol IV are inconsistent at the levels of the music IV. This is what a statistically significant interaction tells you: that there is evidence that the effects of one IV are inconsistent at the levels of other IVs.
Although it might sound odd to be interested in inconsistencies in the effects of our IVs, we are often very interested in evidence that our IVs interact in this way. Indeed, quite often we are more interested in interactions than in the main effects of our IVs. (To find out more about why, see Section C4 of this Web site.)
The differences between cell means (e.g., between Cell Mean A and Cell Mean C, or between Cell Mean B and Cell Mean D) have a name of their own. These differences are called simple effects. So, for example, we would refer to the “simple effects of alcohol at the levels of the music IV.” Interactions occur when the simple effects of an IV differ. Once you know how, you can therefore test simple effects for statistical significance. (For more on testing for simple effects see Section B7.2 of this Web site.)
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