Random Assignment and Causal Claims

A causal claim says the treatment itself produced the outcome, not something else riding along with it. The only way to earn that claim is random assignment: flipping a coin, drawing lots, anything that gives each person the same chance of landing in either group. Do that with enough people, and age, health, motivation, income, every trait you didn't even think to measure, gets scattered roughly evenly on both sides. The groups end up alike in every way except the one thing you controlled, so if the outcomes differ, the treatment is the only explanation left standing.

Let people choose their own group instead, and that balance collapses. In a tutoring study where students decide for themselves whether to join, the students who sign up are probably more motivated, have more support at home, or already care more about their grades. If the tutored group scores higher, you cannot tell whether tutoring helped or whether the kind of student who seeks out tutoring would have scored higher anyway. The groups differ before the study even starts, so the comparison is contaminated from the outset. This is why a causal claim also stays limited to the people actually studied unless they were randomly selected from a wider population, and why dropout during a trial is dangerous: if the sicker patients quit the drug group, the groups stop being comparable, and the clean random split you started with is gone.

Correlation without random assignment proves only that two things move together, never that one drives the other. Ice cream sales and swimming accidents both climb in summer, not because cones cause drownings, but because heat drives both. Spotting that kind of hidden third factor, called a confounding variable, is the main defense against mistaking correlation for causation.