Observational Studies versus Experiments

In an observational study, nobody hands out the treatment. Researchers just watch people who already chose their habits and record what happens. That means any group who drinks more coffee, say, might also differ in other ways: they could exercise more, smoke less, earn more, sleep better. Those other differences, called lurking variables, can drive the outcome while coffee just rides along. The study can report that heavier coffee drinkers lived longer, an association, but it cannot say coffee caused it, because the groups were never comparable to begin with.

An experiment fixes this by using random assignment: the researcher, not the participant, decides who gets the treatment and who doesn't. With enough people, randomization spreads lurking variables evenly across groups, so the groups start out alike in every way except the treatment. Whatever difference shows up at the end has nowhere else to come from. That is the entire logic behind a causal claim, and no amount of sample size fixes its absence. A study of ten thousand self-selected coffee drinkers is still just a bigger observational study; size shrinks random error, not bias from lurking variables.

This splits into two separate questions worth keeping apart: how was the sample chosen, and how was the treatment assigned. Random selection from a population lets a result generalize to that population. Random assignment within the study lets a result support a cause. A study can have one, both, or neither, and knowing which one is missing tells you exactly what the data can and cannot claim.