Harlan N. answered 04/29/17
Tutor
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Masters in Statistics and Analysis Experience
There are two things in your question. First, the treatment is assigned by the researcher. The subjects do not get to choose. Second, the assignment is random. The researcher devises a randomization scheme, then uses it to assign treatment to the patients. The assignment of treatment by the researcher instead of having the subject decide the treatment should solve the correlation/causation problem. It makes any difference observed due to cause/effect not correlation. The randomization removes confounding factors as an explanation. Confounding refers to some other cause not taken into account that is producing the effect.
Unfortunately, nothing is ever guaranteed. For example, I might want to know if ice and water causes people to get drunk. So I give a panel each a bottle of vodka. Then I randomly assign the distribution of ice and water to some of the experimental units. I make sure none of the experimental units are alcoholics. I leave them in a room with their vodka. It turns out that many of the experimental units don't like to drink vodka without ice or water, so they don't drink any vodka. The statistical analysis will show that ice and water make people drunk.