Experiments & Random Assignment
An experiment earns the right to say caused because of one deceptively simple move: random assignment. Deciding who goes in which group by chance, not by choice, convenience, or the researcher's hunch, is the single most powerful idea in research design. It works in a way nothing else quite matches.
The problem: confounds
Suppose a new study-skills workshop looks like it boosts grades. The trouble is, the students who signed up were probably more motivated to begin with. Motivation is a confound: it's tangled up with both the "treatment" (attending) and the outcome (grades), so you can't tell whether the workshop did anything at all. Every self-selected comparison hides confounds like this, and the truly dangerous ones are the confounds you never thought to measure.
Randomization's superpower: flipping a coin to assign each person balances every confound at once — the ones you measured, the ones you forgot, and the ones nobody has ever named — because chance can't know which trait is which. No amount of statistical adjustment can promise that, because you can only adjust for variables you actually recorded.
🎲 Assign the Same People Two Ways
One fixed population of people, each with a visible age (color) and motivation (size), plus a hidden confound you never measured. Let people self-select, or assign them by coin flip, and watch the balance bars. Grow the sample to see what shrinks and what doesn't.
Two lessons jump out of that picture. Under self-selection, every trait tied to who volunteers (motivation, age, and the hidden confound riding along with them) stays stubbornly imbalanced no matter how big the sample gets. Bias doesn't wash out with more data; it just becomes a more precise wrong answer. Under randomization, every bar drifts toward zero as n grows, including the confound you never measured.
Random assignment ≠ random sampling
These two "randoms" do completely different jobs, and mixing them up is one of the most common exam mistakes:
- Random assignment decides which group each participant lands in. It protects internal validity: your confidence that the treatment, not some confound, caused the difference.
- Random sampling decides who gets into the study in the first place, from the wider population. It protects external validity — how far your result generalizes, and it is the subject of sampling methods.
A tightly controlled lab experiment on 40 randomly-assigned undergraduates has strong internal validity but shaky external validity. A big representative survey has the reverse. You want both, but they come from different design choices, and only random assignment licenses causal language.
Control groups and placebos
Randomization needs something to compare against: a control group that experiences everything except the active ingredient. In drug trials that means a placebo (an inert pill), because merely believing you're being treated can move outcomes (the placebo effect). Without a comparison group, you can't separate the treatment's effect from time passing, repeated testing, or hope. The gold-standard phrase, a randomized controlled trial, is just these two ideas bolted together. A placebo only does its job if nobody involved can tell who received it, which is why the third ingredient is blinding.
Why it matters: observational data can be mined forever and still can't settle causation, because the groups differ in ways you can't fully see. Random assignment is the rare tool that handles the unknown unknowns for free. When you can randomize, do — and when you can't, know exactly what you're giving up: that is the subject of quasi-experiments and observational designs, the next two lessons.
Problem 38 of the practice problems is this lesson stated as a press release: an optional module whose users scored nine marks higher, and the question of what a coin flip would have bought.
Common questions
Does random assignment guarantee balanced groups?
Not in every single study. Randomization balances groups in expectation: with a small sample you can still draw an unlucky split where one group happens to be older or more motivated. It just makes such imbalances random rather than systematic, and they shrink as the sample grows. That's still a huge win: unlike self-selection, the imbalance isn't tied to who chose the treatment, and any leftover difference is exactly the kind of chance variation your significance test already accounts for.
How do I actually randomize? Is alternating participants good enough?
Alternating is not randomizing. Any rule a person can predict (every other arrival, odd and even ID numbers, Monday versus Tuesday) can be anticipated by whoever is recruiting, and the moment someone can foresee the next allocation they can consciously or unconsciously steer who turns up for it. Generate the sequence with something genuinely random, in advance, and keep it out of the recruiter's hands until the participant is committed: that second part is allocation concealment, and it is the piece most often missing. Sealed opaque envelopes are the low-tech version and a script that assigns on enrollment is the modern one. For small studies use block randomization, where the sequence is built from blocks that each contain equal numbers of every condition, so the groups cannot drift far apart if you stop early. Report the method you used, because 'participants were randomly assigned' with no detail is exactly the sentence reviewers have learned to distrust.
What is a wait-list control group?
A wait-list control is a comparison group that receives the treatment later, after the study's measurements are done. It's common when withholding a promising intervention entirely would be unfair — everyone eventually gets it, but the delay creates an untreated comparison window. It keeps random assignment intact while sidestepping the ethical problem of a pure no-treatment group, though it can't control for the placebo effect the way an active or placebo control does.