Random sampling vs random assignment
By Jude Wallis · Published
Random sampling is how units get into the study, and it buys generalization to the population they came from. Random assignment is how units in the study get to treatments, and it buys a cause-and-effect conclusion. The two choices are independent, so a study can have both, one, or neither.
AP Statistics: Unit 1 (topics 1.11 Random Sampling, 1.13 Experimental Design). In the Fall 2026 AP Statistics course, random sampling is topic 1.11 and random assignment belongs to experimental design, topic 1.13. Both sit in Unit 1, Exploring One-Variable Data and Collecting Data, which is 20% to 30% of the multiple-choice section, so this pair is worth knowing cold.
Random sampling vs random assignment: the short answer
Two chance devices, used at two different moments, for two different jobs.
Random sampling decides who enters the study. You start with a population, or with the list that stands in for it, and a chance device picks which members get measured. That is a selection step, and it happens before anything is done to anybody.
Random assignment decides what happens to the units already in the study. Once the subjects are in hand, a chance device, not the researcher and not the subject, decides which treatment each one receives. That is an allocation step, and it exists only in experiments.
Each one buys exactly one permission. Random sampling buys the right to talk about the population the sample came from. Random assignment buys the right to say the treatment caused the difference. Neither does the other's job, and the two choices are made independently, so all four combinations exist and each licenses something different.
What random sampling is
Random sampling means a chance device chooses which members of a population go into the sample, so whether you are in the study is settled by a known chance mechanism rather than by anything you or the researcher preferred. A simple random sample is the plain version. Stratified, cluster, and systematic samples put structure around the chance device but keep the selection random; the differences between them are drawn out in simple random vs stratified sampling.
What that buys is an audience. Because nothing systematic decided who got in, the sample carries no built-in tilt, and a sample mean or sample proportion estimates the population value without a systematic error pushing it one way. So a conclusion drawn from the sample extends to the population the sample was drawn from.
Two limits come attached. The reach stops at the list you sampled from rather than the population you had in mind, so a random sample of registered voters says nothing about adults who never registered; that boundary is the sampling frame. And random sampling licenses nothing at all about cause. It fixes who you are talking about, never why the numbers came out the way they did.
Random sampling is topic 1.11 in the Fall 2026 course.
What random assignment is
Random assignment means a chance device decides which experimental unit receives which treatment, and the device's probabilities do not depend on anything about the unit. A coin flip, names from a hat, and a random number generator all qualify. Letting subjects pick their own group, or letting a researcher sort them by who looks suitable, does not.
What that buys is a causal claim. Every variable other than the treatment, the ones you thought of and the ones you never will, was spread across the groups by that same chance mechanism. So a confounding variable cannot be the systematic explanation for a difference in the response. Two explanations survive, the treatment or the luck of the draw, and a p-value weighs the second one: how surprising a gap this large would be if the treatment did nothing.
Balance is a tendency, not a guarantee. Random assignment is judged on the procedure used, not on the split it happened to produce, so a group that came out lopsided on age is not evidence the randomization failed. Reshuffling until the groups look even is what actually breaks it.
Random assignment says nothing about who is in the study. Forty volunteers randomly assigned support a causal claim about people like those forty volunteers and about nobody else. Random assignment belongs to experimental design, topic 1.13.
The differences side by side
One word, random, doing two unrelated jobs.
| Feature | Random sampling | Random assignment |
|---|---|---|
| Question it answers | Who is in the study? | Who gets which treatment? |
| The verb | Select | Assign |
| Where it appears | Surveys and experiments | Experiments only |
| What it rules out | Systematic bias in who was selected | Confounding as the explanation for a difference |
| What it buys | Generalization to the population sampled | Cause and effect |
| What its absence costs | The audience shrinks to units like those studied | The claim weakens to association |
Read the verb row first. If units are being chosen, that is sampling. If treatments are being handed out, that is assignment. The question settles almost every exam item on this pair before you read the rest of the scenario.
All four combinations, and what each one licenses
The two dials are set independently, so a study can have both, either, or neither, and the combination is what decides the sentence you are allowed to write.
| The study's units | Treatments randomly assigned | No random assignment |
|---|---|---|
| Randomly sampled from a population | Cause and effect, for that whole population | Association only, for that whole population |
| Not randomly sampled | Cause and effect, for units like those studied | Association only, for units like those studied |
Both. A hospital system employs 3,100 nurses. A researcher randomly selects 260 of them from the personnel roster, randomly assigns 130 to a structured shift-handoff checklist and 130 to current practice, and counts medication errors over a quarter. A difference in errors can be credited to the checklist, and the finding reaches all 3,100 nurses in that system. This is the strongest cell and the rarest one.
Random sampling only. A state agency randomly selects 500 of its 21,000 licensed food handlers and records whether each wears gloves and how many violations each was cited for. Glove wearers are cited less often. That association describes all 21,000 licensed handlers, because the 500 were drawn at random from the licence list. Nobody assigned gloves, so training, employer, and years on the job all stay live as explanations. Well-run surveys land in this cell.
Random assignment only. Ninety patients answer a flyer posted at one clinic, and each is randomly assigned to one of two inhaler-training videos, 45 and 45. A difference in technique scores can be credited to the video, and the claim covers patients like the ones who answered that flyer. It does not reach asthma patients in general, because nobody sampled them. This is the shape of most published experiments.
Neither. A coding bootcamp compares the 60 students who chose its evening track with the 60 who chose the morning track. Students picked their own group, and the bootcamp enrolled whoever applied. The comparison describes those 120 students and stops there. Evening students may be older, may already work full time, may have written code before, and nothing in the design separates any of that from the schedule.
Why both is rare, and why one is not a failure
Each randomization has its own price. Random sampling needs a list of the population and some way to reach whoever comes up, which is why surveys manage it: reaching someone means asking them a question. Random assignment needs the ethical and practical standing to impose a treatment, which is why experiments manage it, and why no study will randomly assign a family history or twenty years of smoking.
Paying both prices at once means recruiting a randomly chosen stranger off a population list and then putting them in a treatment group, which is usually impractical and often not ethical. So experiments recruit volunteers and get the assignment dial only, while surveys sample carefully and get the selection dial only. The two single-dial cells are the ordinary ones, not the broken ones.
A missing randomization makes the claim narrower, not worthless. The error is never running a volunteer experiment; the error is writing a conclusion wider than the design paid for. Can you generalize results works through the exact wording for each cell, and scope of inference is the name for the whole question.
The classic mix-up and how to avoid it
The mix-up is rarely about the definitions. It is citing one randomization as the reason for the other one's conclusion. Two sentences fix it, each naming the randomization that earns it.
For cause: because the treatments were randomly assigned, the difference in the response can be attributed to the treatment. For audience: because the units were randomly selected from the population, the result extends to that population. Swap the two reasons and the answer is wrong even though every individual word in it is true.
Two sentences never to write. "The sample was large, so the results generalize" credits size for work only random selection does, which is why a bigger sample does not fix bias. "The study was randomized, so it applies to everyone" credits random assignment for work only random sampling does.
The cue is select versus assign, the same cue that separates blocking vs stratifying: you stratify people you are about to select, and you block units you are about to assign. Rehearse the wording in scope of inference practice, and see experiments vs observational studies for the design question that sits underneath it.
One 38-second gap, four different conclusions
A state association registers 8,000 high school cross-country runners. Four studies compare a 10-minute dynamic warmup with the usual static stretch, and all four find the dynamic group improved its 5K time by 46 seconds on average against 8 seconds for the static group. Study A randomly selects 240 runners from the association roster and randomly assigns 120 to each warmup. Study B randomly selects 240 from the roster and records which warmup each runner already uses. Study C takes the 240 runners on four teams whose coaches volunteered and randomly assigns 120 to each warmup. Study D takes those same 240 runners from the volunteering teams and records the warmup each already uses. State what each study may conclude.
Size the effect once, because it is identical in all four: seconds, which is minutes.
Set the two dials for each study. A has random sampling and random assignment. B has random sampling only. C has random assignment only. D has neither.
Study A. Random assignment makes the 38-second gap attributable to the warmup, because the two groups of 120 differ only by the luck of the draw. Random selection of 240 from 8,000, a sampling fraction of or 3%, carries that conclusion to all 8,000 registered runners.
Study B. Runners chose their own warmup, so the 38 seconds is an association: runners on better-coached teams may both improve more and be the ones already doing dynamic warmups. The association still describes all 8,000 registered runners, because the 240 were randomly selected from the roster.
Study C. Random assignment still earns the causal claim, since the split into was made by chance. But the 240 came from four volunteering teams rather than the roster, so the conclusion covers runners like those on those teams and not the other 7,760.
Study D. Neither dial is set. Study D describes 240 runners on four self-selected teams who chose their own warmups, and it cannot rule out that the runners who improve most are the ones who already warm up dynamically.
Read the pattern. The number 38 never changed. What changed was the design, and the design alone decided what could be written.
All four studies find the same 38-second advantage. Study A: the warmup caused it, for all 8,000 registered runners. Study B: an association, for all 8,000. Study C: the warmup caused it, but only for runners like those on the four volunteering teams. Study D: a description of those 240 runners and nothing further.
Adding one randomization at a time
A city has 12,000 households on curbside recycling collection. Version 1: the city mails a sorting guide to the 500 households that requested one, and compares their bin contamination rate with 500 households that did not request it. Version 2: the city takes the 500 households that requested a guide and randomly assigns 250 to receive it and 250 to receive nothing. Version 3: the city randomly selects 500 of the 12,000 households, then randomly assigns 250 to receive the guide and 250 to receive nothing. Every version finds a contamination rate of 11.4% with the guide against 17.9% without. What does each version buy?
Size the gap, which is the same in every version: percentage points.
Version 1 has neither randomization. Households asked for the guide, so they also chose their own group, and households that request a sorting guide are plausibly the ones already trying to sort well. The 6.5 points describe those households and support no causal claim.
Version 2 adds random assignment inside the volunteer pool. The 500 requesters were split by chance alone, so no systematic difference other than the guide separates the groups, and the 6.5-point gap becomes attributable to the guide.
Version 2 buys nothing on audience. Those 500 are still self-selected requesters, so the causal claim covers households like the ones that ask for a guide, and not the city.
Version 3 adds random sampling on top. Drawing 500 of 12,000 is a sampling fraction of , about 4.2%, and that draw does not depend on who wants a guide.
Version 3 has both dials. The guide caused the 6.5-point drop in contamination, and the conclusion reaches all 12,000 households on the collection list. Notice which step did which job: assignment moved the claim from association to cause, and sampling moved the audience from requesters to the whole city.
Version 1 describes 1,000 self-selected households and supports neither a causal claim nor a claim about the city. Version 2 adds random assignment and earns cause and effect, but only for households that ask for a guide. Version 3 adds random sampling on top and earns that same causal claim for all 12,000 households on the list. Each randomization upgraded exactly one half of the conclusion.
Frequently asked questions
Is random sampling the same as random assignment?
No. Random sampling selects which units enter the study, out of a population. Random assignment allocates the units already in the study to treatments. Selection versus allocation. Random sampling buys generalization to the population sampled, random assignment buys a cause-and-effect conclusion, and neither one does the other's job.
Which one do I cite for a causal conclusion?
Random assignment, every time. The causal sentence cites random assignment and the generalization sentence cites random sampling. Naming a control group, a placebo, blinding, or a large sample as the reason a treatment caused an effect earns nothing, because none of those spread the other variables across the groups by chance.
Can an experiment have random assignment without random sampling?
Yes, and most do. Volunteers are recruited, then randomly assigned to treatments. The causal conclusion is fully intact for the people in the study. What is narrow is the audience: the result reaches only individuals similar to the volunteers who took part, which is a smaller claim rather than a broken one.
Does random assignment guarantee the two groups are alike?
No. It spreads every other variable across the groups by chance, so the groups match on average over many repetitions, but any single assignment can land lopsided. That is why random assignment is judged on the procedure used rather than on the split it produced, and why reshuffling until the groups look even destroys the very thing it was meant to protect.
Does a bigger random sample let me claim cause?
No. Sample size controls how precise an estimate is, not what kind of relationship the design supports. With no treatment assigned, a variable associated with both the explanatory and the response variable stays a live alternative explanation no matter how many rows the data set has.