Interaction between two continuous variables

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Statistical programs, like SPSS, do not always have "point-and-click" commands for every possible statistical test. This page is a description of how to test the interaction between two continuous variables. Below, an explanation of interactions is presented, then the three steps to conduct the interaction is described, and examples are given to help in understanding the steps involved.

What is an interaction?


Three Steps

There are three steps involved to calculate the interaction between two continuous variables.

  1. Center the two continuous variables
    • To increase interpretability of interactions numerous researchers (e.g. (Aiken and West, 1991); (Judd and McClelland, 1989)) have recommended centering the predictor variables (X1 and X2). If the variables are not centered there are possible problems with multicolinearity, which means that if the IVs are not centered their product (used in computing the interaction) is highly correlated with the original IV.
    • You center the continuous variables by subtracting the mean score from each data-point. In other words, use SPSS, or another statistical program, to find the mean value of the variable. Then, use the "Compute" command in SPSS to create a new variable that is the original values minus the mean. Then, repeat the procedure for the second variable.
    • As a concrete example, imagine you have 200 subjects (N=200) for which you have their IQ score and the length of time they studied for an exam. Thus, there are two continuous variables (X1=IQ, X2=time spent studying), and your dependent variable is the test score (Y=test score).
    • Imagine that the average IQ score is 100. To center the IQ variable, 100 needs to be subtracted from every every subject's IQ score. So if a subject has an IQ of 115, their centered IQ score is 15. If a subject has an IQ of 90, their centered IQ score is -10. For easy reference, lets called the newly centered IQ score as "IQ_c".
    • To check your transformation has been performed correctly you should compute the mean of your IQ_c variable. If the centering process has worked the mean score for IQ_c should be 0. It is important that the mean score you subtract is as accurate as possible. Typically this means your mean score should be entered to say at least 4 decimal places (though the number of decimal places needed will depend on your data). If you have rounded your mean score your centered variable may not have a mean of zero.






Plotting the interaction

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