Comment by akoboldfrying

> "1 cup of caffeinated coffee" basically says nothing at all

Frankly, no. 1 cup of caffeinated coffee is on average significantly more caffeine than 0 cups, which is all you need for sufficient n. The only confounding variable to worry about here is whether caffeine is entering the diets of the two experimental groups at different rates via other channels (e.g., are the people who are forbidden to drink coffee drinking more tea to compensate?), though even this effect, if present, would likely tend to decrease the separation of the outcome distributions and is thus a low threat to validity.

People obsess over precision when it is often one of the least important aspects of an experiment. The outcomes of studies like this are in practice absolutely dependent on quality and rates of compliance. Choosing an uncomplicated treatment that is easy and natural for subjects to comply with is not merely acceptable but in fact a massively better design than complex protocols involving precisely measured quantities of lab-grown coffee in vials that can be misplaced, forgotten, deliberately shunned, etc. Also in this case the treatment corresponds closely to the real-world situation that the research is attempting to learn about.