Quantitative Results

Statistical Analysis

Moderation and mediation are two very different ideas, so it is a little unfortunate that they not only have such similar names, but also tend to accompany the same citation: Baron and Kenny (1986). While there are a few similarities between the two analyses that are important to understand, here we will focus on the differences between moderation and mediation.

To begin, we do need to understand that both analyses have to do with better understanding the relationship between an independent and dependent variable. In this regard, both mediation and moderation have to do with checking on how a third variable fits into that relationship. For the purposes of understanding these two concepts, this is where the similarities end.

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Moderation is a way to check whether that third variable influences the strength or direction of the relationship between an independent and dependent variable. An easy way to remember this is that the moderator variable might change the strength of a relationship from strong to *moderate*, to nothing at all. It is almost like a turn dial on the relationship; as you change values of the moderator, a statistical relationship that you observed before might dissolve away. For example, if you expected that the length of time studying related to the grades on a calculus test, you would probably be right. Let’s say there is a strong relationship between time spent studying and grades. However, that relationship may not hold true across the board; something like grade level might be a possible moderator. If you switch the value of this moderator from college student to elementary school student, that relationship is not likely to hold up. No amount of studying is likely to help a second grader an A on a calculus exam, but for a college student, study time will matter a great deal.

Mediation is a little more straightforward in its naming convention. A mediator *mediates* the relationship between the independent and dependent variables – explaining the reason for such a relationship to exist. Another way to think about a mediator variable is that it *carries* an effect. In a perfect mediation, an independent variable leads to some kind of change to the mediator variable, which then leads to a change in the dependent variable. However, in practice, the relationships between the independent variable, mediator, and dependent variable are not tested for *causality*, just a correlational relationship.

The purpose of mediation analysis is to see if the influence of the mediator is stronger than the direct influence of the independent variable. An obvious real-life mediator is temperature on a stove. Water will not start to boil until you have turned on your stove, but it is not the stove knob that *causes* the water to boil, it is the heat that results from turning that knob. To test something like this, we could check to see how tightly correlated the knob being turned is to the water’s state (i.e., is it boiling?). For the first few minutes there would be no effect, so we can treat that as a weak correlation. Compared to the relationship between the temperature of your stove top and the state of the water, we can see that it is actually the temperature of the stove (the mediator) that is causing the water to boil, not just the action of turning a knob (the independent variable). Comparing the strength of these effects gives you insight into what is really carrying the effect on the water (the dependent variable).