Random Assignment Examples in Statistics
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Random Assignment.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.
Concept Recap
Random assignment is the process of placing participants into treatment groups by chance. It helps make the groups similar at the start of an experiment so differences at the end are more likely to be caused by the treatment.
Random sampling helps you generalize to a population. Random assignment helps you compare treatments fairly inside an experiment.
Read the full concept explanation âHow to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Random Assignment checks whether the study design supports a fair comparison before interpreting the outcome.
Common stuck point: Students often know a procedure related to random assignment but skip the recognition step: Did the study use a design feature that makes the groups comparable before the outcome is measured? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint: Ask: Did the study use a design feature that makes the groups comparable before the outcome is measured?
Common Mistakes to Watch For
Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.
Worked Examples
Example 1
mediumDesign an experiment to test whether a new fertilizer increases tomato yield. Include random assignment.
Answer
First step
1
List all tomato plots (experimental units).
See the full worked solution + why-it-works coaching
SetupKey insightWhy it worksCommon pitfallConnection
Unlock answer keys One Family plan â every worked solution, all subjects
Example 2
mediumA school has 60 students and wants to test a new reading program against the standard one. Describe how to use random assignment.
Example 3
mediumIdentify which of the following ensures random assignment: (a) volunteers self-select, (b) alternating subjects A, B, A, B by arrival order, (c) coin flip for each subject.
Example 4
hardA college study randomly assigns 200 freshmen to a study-skills workshop or a control. Three months later, GPAs are compared. Is the comparison fair if 30 control students dropped out and 5 treatment students dropped out?
Example 5
hardAn online experiment randomly assigns 50,000 users to two versions of a webpage. After running, the data scientist sees the treatment version has more late-night users. What likely explains this?
Example 6
hardA study with random assignment finds no difference between groups. The researcher concludes the treatment doesn't work. What additional information is needed to evaluate that claim?
Example 7
challengeExplain why a study can have random assignment but still show a biased estimate of treatment effect if the outcome is measured non-blindly.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyIn an experiment, flipping a coin to decide whether each subject gets the drug or placebo is an example of what?
Example 2
easyRandom assignment helps make the treatment and control groups what at the start of an experiment?
Example 3
easyRandom sampling helps you do what, while random assignment helps you do what?
Example 4
easyA teacher lets students pick their own group (treatment or control). Is this random assignment?
Example 5
easyWhy does random assignment let us attribute outcome differences to the treatment?
Example 6
easyDoes random assignment guarantee the groups are exactly identical in every trait?
Example 7
easyWhich requires random assignment: generalizing a poll to all voters, or claiming a drug caused recovery?
Example 8
easyAfter randomly assigning subjects, a researcher swaps a few people between groups to 'balance ages.' Did she preserve random assignment?
Example 9
mediumA trial randomly assigns 200 patients to drug or placebo. Critics say age wasn't balanced perfectly. Is this a fatal flaw of random assignment? Explain.
Example 10
mediumExplain why random assignment can balance confounders the researcher never even measured, unlike statistical adjustment.
Example 11
mediumA study has random assignment but no control group; everyone gets the drug at a random dose. Can it isolate whether the drug works at all? Explain what's still missing.
Example 12
mediumTwo designs: (A) randomly assign smokers and nonsmokers to groups for an unrelated drug; (B) compare smokers vs nonsmokers for lung effects. Which uses random assignment, and which can claim causation about smoking?
Example 13
mediumA coach assigns players to two training methods by jersey number (even vs odd). Argue whether this counts as valid random assignment.
Example 14
mediumA trial randomly assigns treatment but allows patients who feel worse to switch groups mid-study. Explain how this undermines the benefits of the original random assignment.
Example 15
mediumWhy do large experiments rely on random assignment rather than carefully matching subjects on every known variable?
Example 16
challengeIn a randomized trial of 30 patients, by chance the treatment group ends up older on average. Explain whether the causal conclusion is invalid, and what tools address this small-sample imbalance.
Example 17
challengeDistinguish precisely the inferential roles: a study uses random sampling but not random assignment; another uses random assignment but not random sampling. What can each validly claim?
Example 18
challengeA researcher claims that because she randomly assigned treatment, her results automatically generalize to the whole country. Explain the flaw and which random procedure generalization actually requires.
Example 19
mediumA trial assigns the first 50 arrivals to treatment and the next 50 to control. Explain why arrival order may not be true random assignment.
Example 20
mediumExplain why random assignment is what justifies saying a treatment 'caused' an outcome, whereas a strong correlation alone does not.
Example 21
easyA researcher draws names from a hat to decide who gets the new training program and who doesn't. What design feature is this?
Example 22
easyA study assigns subjects to groups based on the first letter of their last name (A-M vs N-Z). Is this random assignment?
Example 23
easyWhich study type uses random assignment: an observational study or an experiment?
Example 24
easyDoes random assignment require that each subject have an equal probability of being in each treatment group?
Example 25
easyAfter randomization, the researcher notices age looks unbalanced and re-randomizes only the older subjects. Is this still random assignment?
Example 26
mediumTwo studies of the same drug: Study A randomly assigns patients; Study B lets patients choose. Both find improvement in the drug group. Which study's causal claim is stronger?
Example 27
mediumRandom assignment is sometimes impossible â for example, you can't randomly assign people to smoke for 20 years. What kind of study fills this gap, and what is its limitation?
Example 28
mediumA blocked design first sorts subjects by sex, then randomly assigns within each block. Is random assignment preserved?
Example 29
mediumA trial randomly assigns 1,000 patients to drug or placebo. The drug group ends up with slightly more men (53% vs 47%). Does this break random assignment?
Example 30
mediumIf a researcher has used random assignment, what type of confounders has it balanced: only the ones they measured, or also unknown ones?
Example 31
mediumIn a randomized experiment with , the researcher finds the treatment group is sicker at baseline. Was random assignment misapplied?
Example 32
mediumAn experiment uses random assignment but the treatment is unblinded and patients can switch groups during the study. What problem does switching create?
Example 33
mediumWhy does random assignment let small but real treatment effects show up against background noise?
Example 34
hardA pharma company recruits patients via a website, then randomly assigns them to drug or placebo. The result generalizes well to whom?
Example 35
hardA teacher randomly assigns classes (not individual students) to a new curriculum. What design is this, and why does it matter for analysis?
Example 36
hardA researcher claims their study has both random sampling and random assignment. What two distinct guarantees does this dual structure provide?
Example 37
hardSuppose 100 patients are randomly assigned to two groups. The probability of any specific 50-50 split is small, yet we trust the randomization. Why?
Example 38
hardA 'natural experiment' uses random or quasi-random variation in policy (e.g., a lottery for school admission). Why is this nearly as good as a designed experiment?
Example 39
challengeAn experiment uses random assignment in a small village; everyone knows who got the treatment, and treated villagers share tips with controls. Why is the causal estimate biased downward, despite valid random assignment?
Related Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.
experimental designpopulation vs sample