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Preamble
In this short exposition, we inquire about the purpose of randomness and how this related to discovering or testing causal inferential problem solving using data and causal models. In his seminal work by Holland (1986) point out something striking that was not put in such form earlier works. He stated the "obvious" that almost all data sets addressing interventional nature, such as treatment vs. non-treatment, that a person or unit we study, can not be treated and not-treated at the same time. We delve question of randomness from this perspective, i.e., so called fundamental problem of causal inference.
Group assignment for causal inference
Group assignment probably one of the most fundamental approach in statistical research, such as in the famous Lady tea tasting problem. The idea of assignment in causal inference, we need to find a matching person or unit that is not-treated if we have a treated sample or the other-way around, so called a matching or balancing.
Randomness in causality: Removal of pseudo-confounders
Randomness doesn't only allow fair representation of control and treatment group assignments, reducing bias essentially. The primary effect of randomness is removal of pseudo-confounders, this is not well studied in the literature. What it means, if we don't randomise there would be other causal connections that would really shouldn't be there.
Conclusion
Here, we hint about something called pseudo-confounders. Randomisation in both matching and other causal techniques primarily removes bias but removal of pseudo-confounders is not commonly mentioned and an open research.
Further reading
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