Stats Make Me Cry - Statistics Blog

I received a great question this week, as a submission to my Ask the Stats Make Me Cry Guy page, which asked: In order for a moderating relationship to exist, do the predictor IV and dependent variable need to be significantly correlated?". This is a question that I am asked a lot, partly because of the common confusion between mediators and moderators and the commonly held belief that an IV and DV should be related for mediation to be present (see my video blog on Mediators, Moderators, and Supressors for more info on this topic). However, moderators are a completely different story. In fact, a simple correlation between two variables can be very misleading, if one relies on it as an indicator of potential moderating effects and/or as an indicator that moderating effects should be tested.

Imagine the circumstance where you are testing whether there is an association between "number of carrots consumed" and "blood pressure". Imagine further that you have reason to believe that the association between these two variables varies by age (for this example let's make age dichotomous, i.e. old vs. young). Perhaps you expect that the more carrots someone eats, the lower their blood pressure will be (negative association), but you think this will be more true for older people than younger (i.e. age moderates the effect of carrot consumption on blood pressure).

Since you'd expect that the association will probably still be negative in both groups, but more negative in older people (if your hypothesis is accurate), you might expect to see a graph like the one below:

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Graphic Example of Moderating Effect in SPSS1
This graph is fairly typical of a two-way interaction, where the two groups (young vs. old) have differing slopes. Since both group's slopes are negative, it isn't supriising that the overall sample slope is also negative. However, imagine a slightly different scenario where younger people's slope was actually positive for some unknown reason. In this case, your graph would look like this:

Graphic Example of Moderating Effect in SPSS 2

In this scenario, you would still likely have significant moderation (probably an even strong interaction effect, since the difference in slope is even larger), however you might not see a significant association between the IV (carrots) and DV (Blood Pressure) in the sample as a whole. This example highlights the danger of relying only on correlations and failing to consider/test potential moderating effects. Thanks for the great question, Ken!
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