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Mediation

Mediation can sometimes be very tricky to a researcher. We think we found an interesting relationship, but then someone points out that a different, more powerful, more explanatory, factor was causing the effect all along! When something like this occurs, we call it mediation!

Example of mediation


Recall in my last post on interactions that I concluded in my fictional study that more hours in my training program were more useful to non-master chess players. A keen observer could have critiqued it by saying, “no no, sir. More overall Chess experience one has, the less errors they will make!” So this critic is saying that “chess experience” is mediating the effect of study hours on mistakes. That is, chess experience in general is explaining why any positive experience occurs from my coaching. So even if they played chess for a while without being coached, they would see a drop in error rate, according to the critic. This might be very true! That’s unfortunate news for my fictional study lab!

The critic’s results would look like this…

The critic’s model for chess errors is actually a lot more reasonable than mine. Why? His is just so much more simplistic. One factor causes another, instead of it being a strange interaction effect that would likely be quadratic (such as people who are novices only gain benefits from coaching if they are very new, but this effect tapers off over time). However, just because it’s easier to understand doesn’t really make it more truthful. It needs to be said, however, that in science we strive to find the most parsimonious answers. That is, we want to use a theory that explains more behavior with less complexity. Easier said than done!!

Alright, so we understand that one factor is the real culprit behind my observed reduction in error rate. What is another way to understand this type of statistical relationship?

This image has been borrowed from a great post on mediation and moderation. If you are interested in the real statistical information behind these effects, check out this site! (http://www.hss.bond.edu.au/stats/public_html/Moderation/mod_notes.htm). As for me, I am just trying to explain what these effects look like more so than the statistical functionality of them.

The chart above shows how we should think about Mediators in statistics. My study observed a relationship between my independent variable (coaching hours) and my dependent variable (mistakes made). When we add the mediator to the model (general chess experience) we see the explanatory power drop down to nearly nothing! Notice the arrow point from the independent variable (coaching) to the mediator (general experience). What this means, once again, is that the useful part of my coaching is that it is chess experience in any form. Mediation is not just a random extra variable, it is an aspect of your independent variable. An aspect of coaching IS experiencing playing chess!! 

In correlations, people often refer to this as a “third variable problem.” In a correlation, you can never tell if an outside factor is influencing your statistical model, or not. Given the complexity of human behavior, you can imagine the amount of grief a mediator could serve to cause a social scientist.

In my next few posts, we will start looking back at social psychology again. I just wanted to share some of the typical statistical terms that you would see and how you can think about them. Also, when someone is talking about a correlation they heard about in a book, or in the news, you can sound like a scientist yourself if you say the following phrase, “while I have no doubt that they observed such a relationship, I am curious about whether or not their statistical model took mediating factors into account. Clearly such other factors could account for such a relationship.” Works every time!

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2 Comments

  1. An interesting example. The chess analogy differs from life and the “life mediator” (if you will) in that the more experience one has in living life does not necessarily result in fewer mistakes made. In fact, how we experience life can reconfirm our erroneous assumptions and cement us further into detrimental and cyclical behavior.

  2. My fictional example is talking expertise with a given set of skills. With any skill, we typically make fewer mistakes as our mastery increases. When we are novices, or even when we are young, we fail to even notice most of the mistakes we made. Once we have gained mastery or enough experience in something, however, our mistakes can seem excessively glaring. This is furthered by confirmation basis. That would be our tendency to only pay attention to evidence that confirms our belief and we ignore the contrary.

    Life experience is a bit broad. In most cases where we see people making these reoccurring mistakes (addictions for example), it is not a simple relationship between number of years living and ability to make good choices. We would have interaction effects! Such as genetic predisposition, attitude towards addictive behaviors, social support, etc.

    When I am referring to a statistical model that has multiple independent variables, I would probably want to use an analysis of variance (anova) or regression models to come to my conclusions instead of correlations. I may revisit statistics in the future and talk about those modeling types, but they tend to be a bit more complicated.

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