Simple main effects (i.e., X leads to Y) are usually not going to get you published. Main effects can be exciting in the early stages of research to show the existence of a new effect, but as a field matures the types of questions that scientists are trying to answer tend to become more nuanced and specific. In this post, I’ll briefly describe the three most common kinds of hypotheses that expand upon simple main effects – at least, the most common ones I’ve seen in my research career in psychology – as well as providing some resources to help you learn about how to test these hypotheses using statistics.

**Incremental Validity**

“Can X predict Y over and above other important predictors?”

This is probably the simplest of the three hypotheses I propose. Basically, you attempt to rule out potential confounding variables by controlling for them in your analysis. We do this because (in many cases) our predictor variables are correlated with each other. This is undesirable from a statistical perspective, but is common with real data. The idea is that we want to see if X can predict unique variance in Y over and above the other variables you include.

In terms of analysis, you are probably going to use some variation of multiple regression or partial correlations. For example, in my own work I’ve shown in the past that friendship intimacy as coded from autobiographical narratives can predict concern for the next generation over and above numerous other variables, such as optimism, depression, and relationship status (Mackinnon et al., 2011).

**Moderation**

“Under what conditions does X lead to Y?”

Of the three techniques I describe, moderation is probably the most tricky to understand. Essentially, it proposes that the size of a relationship between two variables changes depending upon the value of a third variable, known as a “moderator.” For example, in the diagram below you might find a simple main effect that is moderated by sex. That is, the relationship is stronger for men than for women:

With moderation, it is important to note that the moderating variable can be a category (e.g., sex) or it can be a continuous variable (e.g., scores on a personality questionnaire). When a moderator is continuous, usually you’re making statements like: “As the value of the moderator increases, the relationship between X and Y also increases.”

**Mediation **

“Does X predict M, which in turn predicts Y?”

We might know that X leads to Y, but a mediation hypothesis proposes a mediating, or intervening variable. That is, X leads to M, which in turn leads to Y. In the diagram below I use a different way of visually representing things consistent with how people typically report things when using path analysis.

I use mediation a lot in my own research. For example, I’ve published data suggesting the relationship between perfectionism and depression is mediated by relationship conflict (Mackinnon et al., 2012). That is, perfectionism leads to increased conflict, which in turn leads to heightened depression. Another way of saying this is that perfectionism has an indirect effect on depression through conflict.

**Helpful links to get you started testing these hypotheses**

Depending on the nature of your data, there are multiple ways to address each of these hypotheses using statistics. They can also be combined together (e.g., mediated moderation). Nonetheless, a core understanding of these three hypotheses and how to analyze them using statistics is essential for any researcher in the social or health sciences. Below are a few links that might help you get started:

Are you a little rusty with multiple regression? The basics of this technique are required for most common tests of these hypotheses. You might check out this guide as a helpful resource:

https://statistics.laerd.com/spss-tutorials/multiple-regression-using-spss-statistics.php

David Kenny’s Mediation Website provides an excellent overview of mediation and moderation for the beginner.

http://davidakenny.net/cm/mediate.htm

http://davidakenny.net/cm/moderation.htm

Preacher and Haye’s INDIRECT Macro is a great, easy way to implement mediation in SPSS software, and their MODPROBE macro is a useful tool for testing moderation.

http://afhayes.com/spss-sas-and-mplus-macros-and-code.html

If you want to graph the results of your moderation analyses, the excel calculators provided on Jeremy Dawson’s webpage are fantastic, easy-to-use tools:

http://www.jeremydawson.co.uk/slopes.htm

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