There is math for classical causal inference with observational data; that FWIU also hasn't been applied to cognitive outcomes studies.
From "The World Needs Computational Social Science" https://news.ycombinator.com/item?id=37746921 :
> "Answering causal questions using observational data" (2021) [PDF] https://www.nobelprize.org/uploads/2021/10/advanced-economic... https://www.nobelprize.org/prizes/economic-sciences/2021/pop...