Mediation is a theoretical issue in which other factors provide a better explanation for a relationship between two phenomena. Mediation can be investigated with regression analysis.
I suppose most people will say rich people live longer. This theory looks like this:
Between these two aspects a correlation coefficient can be calculated. Most likely a positive correlation coefficient will be found, suppose that r = 0.40. I wrote this number near the arrow.
Someone else can question this theory: people with better access to health care live longer. This theory looks like this:
Again a correlation coefficient can be computed, and suppose now that r = 0.50.
Then the person continues his theory and states: people who are rich can pay for healthcare and that is the reason why the age of dying of rich people is higher. As a matter of fact, he continues, rich people do not live longer if the access to healthcare is taken into account. This theory can be tested with regression. In a diagram the theory looks like this:
Notice that there is a statistically significant relation between all aspects, also between the amount of money in the bank account and access to healthcare. We noted the relationships between the aspects with correlations, whereas regression coefficients can be used too and in the past this was the standard. In my opinion it is better to present correlations, because they are easier to interpret and the single product moment correlation coefficients can be replaced with the multiple correlation coefficients in case a group of variables is used instead of a single one.
To investigate if mediation occurs, the correlation between amount of money in the bank account and age of dying should change from 0.40 to 0.00. This can be tested with hierarchical regression. The two equations to be compared are:
y = a + b1 * x1
y = a + b1 * x1 + b2 * x2
The dependent variable is age of dying (y). In the first equation only access to healthcare (x1) is in the regression analysis and in the second equation amount of money in the bank account (x2) is added. In case that adding the variable money in the bank account has no effect (ΔR2 = 0), there is full mediation. This variable became completely redundant. It supports the theory that rich people don’t live longer because they have more money; access to the healthcare is the one and only reason why people live longer.
In the case that 'money in the bank account' still has effect, ΔR2 is still statistically significant, there is partial mediation. The exact magnitude of the effect can be investigated by calculating the partial correlation coefficients.