4. Example of the Difference between Moderation and Mediation

This example illustrates the importance of clearly specifying your theory in terms of moderators and mediators.

It's taken from an advisory session with a PhD student who approached me to discuss how to test her theory. Her project was looking at the link between language deficit and self-esteem in young adults.

Her hypothesis was that the effects of language deficit on self-esteem were caused by language deficit increasing shyness which in turn decreased self-esteem.

effect of language deficit on self-esteem mediated by shyness

Here's a path diagram for the theoretical model. It suggests language deficit causes shyness, which in turn reduces self-esteem. However, it's a partial mediation model. So this is saying that part of the effect of language impairment on self-esteem is because it can increase people's shyness which in turn reduces self-esteem. The model also indicates a direct effect of language deficit on self-esteem which comprises all the other causes of language deficit effects on self-esteem which are not a part of this shyness model. This direct path includes all unspecified indirect effects as well as a direct effect.

So her theory stated mediated effect and a mediation analysis was required to be performed. (I cover how to do this later).

However, her original proposal was to use ANOVA in the classic way to test main effects of language deficit and shyness and an interaction term. So the theoretical model she was assuming was in fact a moderation effect not a mediation. Here's what the ANOVA model looks like.

effect of language deficit on self-esteem moderated by shyness

Note that this model is not specifying that the effect of language deficit on self-esteem is through shyness. Rather by taking a default ANOVA model the assumed theory is that Shyness has an additional effect on self-esteem, beside language deficit. So when people who are language impaired happen also to be shy people – for whatever reason – they have even lower self-esteem. But we're not testing here that language deficit causes shyness. Shyness may occur for independent reasons. That's different from saying people who are language impaired have lower self-esteem. because they are more shy.

So you need to be careful to ensure that your form of analysis – mediation or moderation – matches your theoretical model precisely.

NEXT: 5. Example of a Basic Test of Mediation

Statistics Training: Introduction to Path Analysis

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