In 1973, Eugene Hammel, an associate dean at the University of California, noticed a worrisome trend in the university’s admission rates for men and women. According to his data, it is shown that 44 percent of the men who applied to graduate school at Berkeley had been accepted, compared to only 35 percent of the women.
After a careful investigation, Eugene found out that even though for each apartment, the admissions decisions were consistently more favorable to women than to men, the admission rate for women is lower than that of men.
The causal story Eugene discovered is that women were rejected in greater numbers because they applied to harder departments to get into, like history and literature, therefore having a lower acceptance rate.

Berkeley Admissions Paradox

Mediation analysis is a causal analysis technique used to assess and measure the impact of different "pathways" and "mechanisms" by disentangling and differentiating between direct effect and indirect effect. As such, it serves to distinguish whether an outcome is caused directly in response to the variable of interest (the direct effect), or through mediators (the indirect effect). Assessing the counterfactuals of the situation can be a notable part of the process.

Mediation Analysis

We want to ask certain typical questions about a mediator: Does it account for the entire effect? Does Drug B work exclusively through blood pressure or perhaps through other mechanisms as well? 
The answer depends on whether the observed salary disparity is produced directly in response to the applicant’s sex or indirectly, through a mediator such as qualification, over which the employer has no control. All the above questions require a sensitive ability to tease apart total effects, direct effects (which do not pass through a mediator), and indirect effects (which do).

University of Michigan - Ann Arbor

The mediator is a variable that functions as the mechanism by way of transferring an effect of one thing to another.  

Consider the chain junction, where $A -> B -> C$.  $B$ is the mediator that transfers the effect of $A$ to $C$.   In other words, the mediator, $B$, is the variable that explains the causal effect of $A$ on $C$.  $A$ can be an indirect cause of $C$, meaning that $A$ affects $B$, which in turn contributes to the change in $C$.  

Mediator

Pearl, J., & Mackenzie, D. (2018). $\mathit{The \ Book \ of \ Why: \ The \ New \ Science \ of \ Cause \ and \ Effect.}$ Basic Books.

The Book of Why

A proxy is used as a substitute measure when a variable that is not directly measurable is needed for analysis.  For a variable to be a proxy for another variable, the proxy variable needs to be highly correlated with the variable of interest.  The proxy can be used for any variables such as a mediator, confounder, collider.  

Proxy

Mediation

A placebo effect is a positive outcome resulting from a simulated treatment, driven largely by an individual's expectation that they will improve. Holding the expectation of recovery can autonomously lead to physiological and psychological benefits, such as reduced stress, lower anxiety and depression, and enhanced immune system functioning, even without an active intervention.

Learn Before

Related

Learn After