Experiments & Random Assignment
An experiment can say caused because of one simple step: random assignment. Deciding who goes in which group by chance, not by choice, convenience, or the researcher's hunch, is the most powerful idea in research design.
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 most dangerous ones are the confounds you never thought to measure.
Why randomization works: flipping a coin to assign each person balances every confound at once (the ones you measured, the ones you forgot, and ones not yet identified). A coin flip is unrelated to every trait a person has, so no trait can be systematically tied to the groups. 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.
The picture shows two things. Under self-selection, every trait tied to who volunteers (motivation, age, and the hidden confound that goes with them) stays imbalanced no matter how big the sample gets. More data does not remove bias. It only makes the wrong answer more precise. 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 is 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, which 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 design, the randomized controlled trial, combines these two ideas. A placebo works as a control only if the participants and researchers cannot tell who received it, so the third ingredient is blinding.
Why it matters: however much observational data you analyze, it can't settle causation, because the groups differ in ways you can't fully see. Random assignment balances even the confounds you don't know about, at no extra cost. When you can randomize, do. When you can't, know what you're giving up. Quasi-experiments and observational designs, the next two lessons, cover that.
Problem 95 of the practice problems applies this lesson to a press release: users of an optional module scored nine marks higher, and the problem asks what a coin flip would have changed.
The short version, set beside the sampling designs it is usually confused with, is in Stats 1: Producing Data & Sampling Design covers randomized comparative experiments, blocking and matched pairs.
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 still matters a great deal. Unlike under self-selection, the imbalance isn't tied to who chose the treatment, and any leftover difference is chance variation of the kind your significance test already accounts for.
How do I actually randomize? Is alternating participants good enough?
Alternating is not randomizing. Whoever is recruiting can anticipate any predictable rule (every other arrival, odd and even ID numbers, Monday versus Tuesday). Once someone can foresee the next allocation, they can consciously or unconsciously steer who turns up for it. Generate the sequence randomly, 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 reviewers have learned to distrust 'participants were randomly assigned' with no detail.
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.