Moderation and Mediation

Both terms are frequently encountered in research papers, textbooks and many reading materials students need to read at university. Unfortunately, students frequently misunderstand, misinterpret and simply confuse them. This confusion should be avoided since the understanding of moderation and mediation is critical for understanding research evidence.
What is moderation? 
Moderation occurs when the relationship between two variables (factors) depends on a third variable (factor). Imagine that we have two variables: variable A: smoking and variable B: cancer.
Smoking is here an independent variable (often abbreviated as IV) and cancer is here a dependent variable (frequently abbreviated as DV). We can also say that we have here a predictor variable (smoking) and an outcome variable (cancer).
We all know that smoking leads to cancer (which is the outcome of smoking). Yet, it is also conceivable (possible) that this relationship is more complex than that.
It is possible that other variable influences the relation between smoking and cancer. For example, patients’ age, sex or exercise level. So smoking can result in different outcomes for participants who differ as far as sex, age and exercise level are concerned. This additional variable is often called the moderator variable or simply the moderator. If moderation occurs, we often say that there is an interaction between the moderator and independent and dependent variables. The interaction can be presented in statistical models and their graphical representations.
Why are moderators important? 
We can say, that moderators provide a more nuanced (detailed) view of the relationship between a dependent and independent variable. In some cases, the moderator can change completely our understanding of the relationship between independent (IV) and dependent (DV) variables. There might exist a statistical relationship between smoking and cancer but it might completely disappear when the third moderator variable is taken into account (or accounted for).
Another example, I might think and hope, that there is a relationship between my new great teaching method and my students’ results. However, if I consider and investigate the influence of the moderator variable – the time students spent on learning). I can disappointingly discover that there is no association whatsoever between my new teaching method and the students’ results. So we can say that the moderator variable has the potential to nullify (cancel out) the association between two variables.
What about mediation and mediator?
Mediation and mediator are similarly looking and sounding terms to already dissuaded words: moderate and moderator. Even worse, these terms are sometimes used interchangeably in researcher. However, mediation and moderation have different meanings in statistical research and different statistical methods are used to investigate them.
What is the difference?  
As I said, the moderator provides evidence of the existence of relation or association between independent and dependent variables. So, we know that the moderator variable affects the relation between IV and DV variables. Now the mediator provides information on how the mediating variable affects this relationship. It shows, how strong the association/the influence on the DV is (look for the regression coefficient). Mediators are often used in multiple linear regression, structural equation modeling (path evaluation).
Let’s look at some examples in psychological and educational research

 ‘the quality of preschool classrooms moderated the association between home environment quality and children’s language and early literacy skills – but not communication skills’

In this example, the quality of teaching in kindergarten (moderator) moderated (influenced) the association between home environment (independent variable) children’s languages skills (dependent variable), and early literacy skills (another dependent variable). However, there was no moderating effect between the quality of teaching in kindergarten (moderator variable) and children’s communication skills (dependent variable).

  ‘In addition, this effect was not found to be moderated by the grade level of students (∆-2LL = 1.40, df = 1, p = .237)’

In this example, we don’t know what effect the researcher is referring to. However, we know that the effect (which is incidentally a dependent variable) is not moderated by the grade level. So the outcomes are not different for children who are in Grade 4 and let’s say Grade 5. It is important to note the p-value, which informs us about the lack of statistically significant moderation.
Last example

All three multiple regression analyses for TWKM, R2 = .524, F(2, 75) = 41.335, p < .001; PPVT–III, R2 = .675, F(2, 73) = 75.946, p < .001; and LCM, R2 = .644, F(2, 73) = 25.80, p < .001, were statistically significant, as were the paths from the mediator to the dependent variable.

Here the researcher looked at the effect of the mediator on the dependent variable. We know that is was were statistically significant, however, we don’t know the strength of the effect which should be provided somewhere else in a paper.