A Randomized Controlled Trial (RCT) or a Controlled Experiment is a method to eliminate unmeasurable confounders effect on causal inference by implementing an intervention on a randomly selected group of individuals (treatment/intervened group) while keeping other individuals unchanged (controlled group, placebo, not-intervened group) to observe the changes in outcomes due to the intervention effect. The RCTs are intended to "disarm" confounders (confounding variables).

Randomized Controlled Trial (RCT) = Controlled Experiment

"What will happen if we *change* the environment?"
"What if we do..."
Ex: What is the probability we get an A on our next Python exam given we increase our daily study hours?
$ P(AGrade| do(hours))  $


"How?"
Ex: "How many more daily hours should I dedicate to exam study?"

University of Michigan - Ann Arbor

Intervention refers to evaluating possible outcomes of a situation with some imposed condition.

Intervention

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

The Book of Why

Common Questions of Intervention

The intervention causes the variable to become unrelated to factors that usually affect it so the arrows between these factors and the variables will not exist in the causal diagram with the intervention.

Intervention in Causal Diagrams

In the context of Berkeley's admission paradox, Bickel contends that discrimination is to do with making decisions that are influenced by the sex of the applicant, even if it is immaterial for the admission decision.  The words like "exercise of decision," "influence," and "immaterial" are suggestive of causation, either belonging to the second (intervention)or third (counterfactuals) Ladder of Causation.  

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